Problem Set 4
2025-03-15
For this assignment, you will use the Caravan dataset from the ISLR2 library. This dataset contains 86 features describing 5822 customer records as it relates to them purchasing insurance. The goal of this analysis will be predict whether or not a customer made the purchase.
Problem 1
Part A
Separate the data into two sets for training and testing.
data(Caravan)
str(Caravan)## 'data.frame': 5822 obs. of 86 variables:
## $ MOSTYPE : num 33 37 37 9 40 23 39 33 33 11 ...
## $ MAANTHUI: num 1 1 1 1 1 1 2 1 1 2 ...
## $ MGEMOMV : num 3 2 2 3 4 2 3 2 2 3 ...
## $ MGEMLEEF: num 2 2 2 3 2 1 2 3 4 3 ...
## $ MOSHOOFD: num 8 8 8 3 10 5 9 8 8 3 ...
## $ MGODRK : num 0 1 0 2 1 0 2 0 0 3 ...
## $ MGODPR : num 5 4 4 3 4 5 2 7 1 5 ...
## $ MGODOV : num 1 1 2 2 1 0 0 0 3 0 ...
## $ MGODGE : num 3 4 4 4 4 5 5 2 6 2 ...
## $ MRELGE : num 7 6 3 5 7 0 7 7 6 7 ...
## $ MRELSA : num 0 2 2 2 1 6 2 2 0 0 ...
## $ MRELOV : num 2 2 4 2 2 3 0 0 3 2 ...
## $ MFALLEEN: num 1 0 4 2 2 3 0 0 3 2 ...
## $ MFGEKIND: num 2 4 4 3 4 5 3 5 3 2 ...
## $ MFWEKIND: num 6 5 2 4 4 2 6 4 3 6 ...
## $ MOPLHOOG: num 1 0 0 3 5 0 0 0 0 0 ...
## $ MOPLMIDD: num 2 5 5 4 4 5 4 3 1 4 ...
## $ MOPLLAAG: num 7 4 4 2 0 4 5 6 8 5 ...
## $ MBERHOOG: num 1 0 0 4 0 2 0 2 1 2 ...
## $ MBERZELF: num 0 0 0 0 5 0 0 0 1 0 ...
## $ MBERBOER: num 1 0 0 0 4 0 0 0 0 0 ...
## $ MBERMIDD: num 2 5 7 3 0 4 4 2 1 3 ...
## $ MBERARBG: num 5 0 0 1 0 2 1 5 8 3 ...
## $ MBERARBO: num 2 4 2 2 0 2 5 2 1 3 ...
## $ MSKA : num 1 0 0 3 9 2 0 2 1 1 ...
## $ MSKB1 : num 1 2 5 2 0 2 1 1 1 2 ...
## $ MSKB2 : num 2 3 0 1 0 2 4 2 0 1 ...
## $ MSKC : num 6 5 4 4 0 4 5 5 8 4 ...
## $ MSKD : num 1 0 0 0 0 2 0 2 1 2 ...
## $ MHHUUR : num 1 2 7 5 4 9 6 0 9 0 ...
## $ MHKOOP : num 8 7 2 4 5 0 3 9 0 9 ...
## $ MAUT1 : num 8 7 7 9 6 5 8 4 5 6 ...
## $ MAUT2 : num 0 1 0 0 2 3 0 4 2 1 ...
## $ MAUT0 : num 1 2 2 0 1 3 1 2 3 2 ...
## $ MZFONDS : num 8 6 9 7 5 9 9 6 7 6 ...
## $ MZPART : num 1 3 0 2 4 0 0 3 2 3 ...
## $ MINKM30 : num 0 2 4 1 0 5 4 2 7 2 ...
## $ MINK3045: num 4 0 5 5 0 2 3 5 2 3 ...
## $ MINK4575: num 5 5 0 3 9 3 3 3 1 3 ...
## $ MINK7512: num 0 2 0 0 0 0 0 0 0 1 ...
## $ MINK123M: num 0 0 0 0 0 0 0 0 0 0 ...
## $ MINKGEM : num 4 5 3 4 6 3 3 3 2 4 ...
## $ MKOOPKLA: num 3 4 4 4 3 3 5 3 3 7 ...
## $ PWAPART : num 0 2 2 0 0 0 0 0 0 2 ...
## $ PWABEDR : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PWALAND : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PPERSAUT: num 6 0 6 6 0 6 6 0 5 0 ...
## $ PBESAUT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PMOTSCO : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PVRAAUT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PAANHANG: num 0 0 0 0 0 0 0 0 0 0 ...
## $ PTRACTOR: num 0 0 0 0 0 0 0 0 0 0 ...
## $ PWERKT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PBROM : num 0 0 0 0 0 0 0 3 0 0 ...
## $ PLEVEN : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PPERSONG: num 0 0 0 0 0 0 0 0 0 0 ...
## $ PGEZONG : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PWAOREG : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PBRAND : num 5 2 2 2 6 0 0 0 0 3 ...
## $ PZEILPL : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PPLEZIER: num 0 0 0 0 0 0 0 0 0 0 ...
## $ PFIETS : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PINBOED : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PBYSTAND: num 0 0 0 0 0 0 0 0 0 0 ...
## $ AWAPART : num 0 2 1 0 0 0 0 0 0 1 ...
## $ AWABEDR : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AWALAND : num 0 0 0 0 0 0 0 0 0 0 ...
## $ APERSAUT: num 1 0 1 1 0 1 1 0 1 0 ...
## $ ABESAUT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AMOTSCO : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AVRAAUT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AAANHANG: num 0 0 0 0 0 0 0 0 0 0 ...
## $ ATRACTOR: num 0 0 0 0 0 0 0 0 0 0 ...
## $ AWERKT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ ABROM : num 0 0 0 0 0 0 0 1 0 0 ...
## $ ALEVEN : num 0 0 0 0 0 0 0 0 0 0 ...
## $ APERSONG: num 0 0 0 0 0 0 0 0 0 0 ...
## $ AGEZONG : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AWAOREG : num 0 0 0 0 0 0 0 0 0 0 ...
## $ ABRAND : num 1 1 1 1 1 0 0 0 0 1 ...
## $ AZEILPL : num 0 0 0 0 0 0 0 0 0 0 ...
## $ APLEZIER: num 0 0 0 0 0 0 0 0 0 0 ...
## $ AFIETS : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AINBOED : num 0 0 0 0 0 0 0 0 0 0 ...
## $ ABYSTAND: num 0 0 0 0 0 0 0 0 0 0 ...
## $ Purchase: Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...head(Caravan)## MOSTYPE MAANTHUI MGEMOMV MGEMLEEF MOSHOOFD MGODRK MGODPR MGODOV MGODGE MRELGE
## 1 33 1 3 2 8 0 5 1 3 7
## 2 37 1 2 2 8 1 4 1 4 6
## 3 37 1 2 2 8 0 4 2 4 3
## 4 9 1 3 3 3 2 3 2 4 5
## 5 40 1 4 2 10 1 4 1 4 7
## 6 23 1 2 1 5 0 5 0 5 0
## MRELSA MRELOV MFALLEEN MFGEKIND MFWEKIND MOPLHOOG MOPLMIDD MOPLLAAG MBERHOOG
## 1 0 2 1 2 6 1 2 7 1
## 2 2 2 0 4 5 0 5 4 0
## 3 2 4 4 4 2 0 5 4 0
## 4 2 2 2 3 4 3 4 2 4
## 5 1 2 2 4 4 5 4 0 0
## 6 6 3 3 5 2 0 5 4 2
## MBERZELF MBERBOER MBERMIDD MBERARBG MBERARBO MSKA MSKB1 MSKB2 MSKC MSKD
## 1 0 1 2 5 2 1 1 2 6 1
## 2 0 0 5 0 4 0 2 3 5 0
## 3 0 0 7 0 2 0 5 0 4 0
## 4 0 0 3 1 2 3 2 1 4 0
## 5 5 4 0 0 0 9 0 0 0 0
## 6 0 0 4 2 2 2 2 2 4 2
## MHHUUR MHKOOP MAUT1 MAUT2 MAUT0 MZFONDS MZPART MINKM30 MINK3045 MINK4575
## 1 1 8 8 0 1 8 1 0 4 5
## 2 2 7 7 1 2 6 3 2 0 5
## 3 7 2 7 0 2 9 0 4 5 0
## 4 5 4 9 0 0 7 2 1 5 3
## 5 4 5 6 2 1 5 4 0 0 9
## 6 9 0 5 3 3 9 0 5 2 3
## MINK7512 MINK123M MINKGEM MKOOPKLA PWAPART PWABEDR PWALAND PPERSAUT PBESAUT
## 1 0 0 4 3 0 0 0 6 0
## 2 2 0 5 4 2 0 0 0 0
## 3 0 0 3 4 2 0 0 6 0
## 4 0 0 4 4 0 0 0 6 0
## 5 0 0 6 3 0 0 0 0 0
## 6 0 0 3 3 0 0 0 6 0
## PMOTSCO PVRAAUT PAANHANG PTRACTOR PWERKT PBROM PLEVEN PPERSONG PGEZONG
## 1 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0 0 0
## 4 0 0 0 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0 0 0
## PWAOREG PBRAND PZEILPL PPLEZIER PFIETS PINBOED PBYSTAND AWAPART AWABEDR
## 1 0 5 0 0 0 0 0 0 0
## 2 0 2 0 0 0 0 0 2 0
## 3 0 2 0 0 0 0 0 1 0
## 4 0 2 0 0 0 0 0 0 0
## 5 0 6 0 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0 0 0
## AWALAND APERSAUT ABESAUT AMOTSCO AVRAAUT AAANHANG ATRACTOR AWERKT ABROM
## 1 0 1 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0
## 3 0 1 0 0 0 0 0 0 0
## 4 0 1 0 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0 0 0
## 6 0 1 0 0 0 0 0 0 0
## ALEVEN APERSONG AGEZONG AWAOREG ABRAND AZEILPL APLEZIER AFIETS AINBOED
## 1 0 0 0 0 1 0 0 0 0
## 2 0 0 0 0 1 0 0 0 0
## 3 0 0 0 0 1 0 0 0 0
## 4 0 0 0 0 1 0 0 0 0
## 5 0 0 0 0 1 0 0 0 0
## 6 0 0 0 0 0 0 0 0 0
## ABYSTAND Purchase
## 1 0 No
## 2 0 No
## 3 0 No
## 4 0 No
## 5 0 No
## 6 0 Nodf.train = Caravan[1:1000, ]
df.test = Caravan[1001:nrow(Caravan), ]
y = df.test$PurchasePart B
Fit a decision tree to the data. Using cross-validation, determine the optimal complexity parameter. Make a plot of the tree, and comment on the number of nodes and depth.
set.seed(100) # set seed
model1 = rpart(Purchase ~ ., data=df.train, cp=0)
rpart.plot(model1)
yhat1 = predict(model1, df.test, type="class")
accuracy1 = mean(y == yhat1)
error_rate1 = 1 - accuracy1
print(paste("Classification error rate:", round(error_rate1, 4)))## [1] "Classification error rate: 0.078"# D: determine optimal cp
grid = expand.grid(cp = seq(0,0.001,by=0.001))
control = trainControl(method="cv", number=5)
model2 = train(Purchase ~ ., data=df.train,
tuneGrid = grid,
trControl = control,
method = "rpart")
# Plot cross-validation results
plot(model2)
# Get the optimal CP value
best_cp = model2$bestTune$cp
print(paste("Optimal complexity parameter (cp):", best_cp))## [1] "Optimal complexity parameter (cp): 0.001"# Get Tree information
print(summary(model2$finalModel))## Call:
## (function (formula, data, weights, subset, na.action = na.rpart,
## method, model = FALSE, x = FALSE, y = TRUE, parms, control,
## cost, ...)
## {
## Call <- match.call()
## if (is.data.frame(model)) {
## m <- model
## model <- FALSE
## }
## else {
## indx <- match(c("formula", "data", "weights", "subset"),
## names(Call), nomatch = 0)
## if (indx[1] == 0)
## stop("a 'formula' argument is required")
## temp <- Call[c(1, indx)]
## temp$na.action <- na.action
## temp[[1]] <- quote(stats::model.frame)
## m <- eval.parent(temp)
## }
## Terms <- attr(m, "terms")
## if (any(attr(Terms, "order") > 1))
## stop("Trees cannot handle interaction terms")
## Y <- model.response(m)
## wt <- model.weights(m)
## if (any(wt < 0))
## stop("negative weights not allowed")
## if (!length(wt))
## wt <- rep(1, nrow(m))
## offset <- model.offset(m)
## X <- rpart.matrix(m)
## nobs <- nrow(X)
## nvar <- ncol(X)
## if (missing(method)) {
## method <- if (is.factor(Y) || is.character(Y))
## "class"
## else if (inherits(Y, "Surv"))
## "exp"
## else if (is.matrix(Y))
## "poisson"
## else "anova"
## }
## if (is.list(method)) {
## mlist <- method
## method <- "user"
## init <- if (missing(parms))
## mlist$init(Y, offset, wt = wt)
## else mlist$init(Y, offset, parms, wt)
## keep <- rpartcallback(mlist, nobs, init)
## method.int <- 4
## parms <- init$parms
## }
## else {
## method.int <- pmatch(method, c("anova", "poisson", "class",
## "exp"))
## if (is.na(method.int))
## stop("Invalid method")
## method <- c("anova", "poisson", "class", "exp")[method.int]
## if (method.int == 4)
## method.int <- 2
## init <- if (missing(parms))
## get(paste("rpart", method, sep = "."), envir = environment())(Y,
## offset, , wt)
## else get(paste("rpart", method, sep = "."), envir = environment())(Y,
## offset, parms, wt)
## ns <- asNamespace("rpart")
## if (!is.null(init$print))
## environment(init$print) <- ns
## if (!is.null(init$summary))
## environment(init$summary) <- ns
## if (!is.null(init$text))
## environment(init$text) <- ns
## }
## Y <- init$y
## xlevels <- .getXlevels(Terms, m)
## cats <- rep(0, ncol(X))
## if (!is.null(xlevels)) {
## indx <- match(names(xlevels), colnames(X), nomatch = 0)
## cats[indx] <- (unlist(lapply(xlevels, length)))[indx >
## 0]
## }
## extraArgs <- list(...)
## if (length(extraArgs)) {
## controlargs <- names(formals(rpart.control))
## indx <- match(names(extraArgs), controlargs, nomatch = 0)
## if (any(indx == 0))
## stop(gettextf("Argument %s not matched", names(extraArgs)[indx ==
## 0]), domain = NA)
## }
## controls <- rpart.control(...)
## if (!missing(control))
## controls[names(control)] <- control
## xval <- controls$xval
## if (is.null(xval) || (length(xval) == 1 && xval == 0) ||
## method == "user") {
## xgroups <- 0
## xval <- 0
## }
## else if (length(xval) == 1) {
## xgroups <- sample(rep(1:xval, length.out = nobs), nobs,
## replace = FALSE)
## }
## else if (length(xval) == nobs) {
## xgroups <- xval
## xval <- length(unique(xgroups))
## }
## else {
## if (!is.null(attr(m, "na.action"))) {
## temp <- as.integer(attr(m, "na.action"))
## xval <- xval[-temp]
## if (length(xval) == nobs) {
## xgroups <- xval
## xval <- length(unique(xgroups))
## }
## else stop("Wrong length for 'xval'")
## }
## else stop("Wrong length for 'xval'")
## }
## if (missing(cost))
## cost <- rep(1, nvar)
## else {
## if (length(cost) != nvar)
## stop("Cost vector is the wrong length")
## if (any(cost <= 0))
## stop("Cost vector must be positive")
## }
## tfun <- function(x) if (is.matrix(x))
## rep(is.ordered(x), ncol(x))
## else is.ordered(x)
## labs <- sub("^`(.*)`$", "\\1", attr(Terms, "term.labels"))
## isord <- unlist(lapply(m[labs], tfun))
## storage.mode(X) <- "double"
## storage.mode(wt) <- "double"
## temp <- as.double(unlist(init$parms))
## if (!length(temp))
## temp <- 0
## rpfit <- .Call(C_rpart, ncat = as.integer(cats * !isord),
## method = as.integer(method.int), as.double(unlist(controls)),
## temp, as.integer(xval), as.integer(xgroups), as.double(t(init$y)),
## X, wt, as.integer(init$numy), as.double(cost))
## nsplit <- nrow(rpfit$isplit)
## ncat <- if (!is.null(rpfit$csplit))
## nrow(rpfit$csplit)
## else 0
## if (nsplit == 0)
## xval <- 0
## numcp <- ncol(rpfit$cptable)
## temp <- if (nrow(rpfit$cptable) == 3)
## c("CP", "nsplit", "rel error")
## else c("CP", "nsplit", "rel error", "xerror", "xstd")
## dimnames(rpfit$cptable) <- list(temp, 1:numcp)
## tname <- c("<leaf>", colnames(X))
## splits <- matrix(c(rpfit$isplit[, 2:3], rpfit$dsplit), ncol = 5,
## dimnames = list(tname[rpfit$isplit[, 1] + 1], c("count",
## "ncat", "improve", "index", "adj")))
## index <- rpfit$inode[, 2]
## nadd <- sum(isord[rpfit$isplit[, 1]])
## if (nadd > 0) {
## newc <- matrix(0, nadd, max(cats))
## cvar <- rpfit$isplit[, 1]
## indx <- isord[cvar]
## cdir <- splits[indx, 2]
## ccut <- floor(splits[indx, 4])
## splits[indx, 2] <- cats[cvar[indx]]
## splits[indx, 4] <- ncat + 1:nadd
## for (i in 1:nadd) {
## newc[i, 1:(cats[(cvar[indx])[i]])] <- -as.integer(cdir[i])
## newc[i, 1:ccut[i]] <- as.integer(cdir[i])
## }
## catmat <- if (ncat == 0)
## newc
## else {
## cs <- rpfit$csplit
## ncs <- ncol(cs)
## ncc <- ncol(newc)
## if (ncs < ncc)
## cs <- cbind(cs, matrix(0, nrow(cs), ncc - ncs))
## rbind(cs, newc)
## }
## ncat <- ncat + nadd
## }
## else catmat <- rpfit$csplit
## if (nsplit == 0) {
## frame <- data.frame(row.names = 1, var = "<leaf>", n = rpfit$inode[,
## 5], wt = rpfit$dnode[, 3], dev = rpfit$dnode[, 1],
## yval = rpfit$dnode[, 4], complexity = rpfit$dnode[,
## 2], ncompete = 0, nsurrogate = 0)
## }
## else {
## temp <- ifelse(index == 0, 1, index)
## svar <- ifelse(index == 0, 0, rpfit$isplit[temp, 1])
## frame <- data.frame(row.names = rpfit$inode[, 1], var = tname[svar +
## 1], n = rpfit$inode[, 5], wt = rpfit$dnode[, 3],
## dev = rpfit$dnode[, 1], yval = rpfit$dnode[, 4],
## complexity = rpfit$dnode[, 2], ncompete = pmax(0,
## rpfit$inode[, 3] - 1), nsurrogate = rpfit$inode[,
## 4])
## }
## if (method.int == 3) {
## numclass <- init$numresp - 2
## nodeprob <- rpfit$dnode[, numclass + 5]/sum(wt)
## temp <- pmax(1, init$counts)
## temp <- rpfit$dnode[, 4 + (1:numclass)] %*% diag(init$parms$prior/temp)
## yprob <- temp/rowSums(temp)
## yval2 <- matrix(rpfit$dnode[, 4 + (0:numclass)], ncol = numclass +
## 1)
## frame$yval2 <- cbind(yval2, yprob, nodeprob)
## }
## else if (init$numresp > 1)
## frame$yval2 <- rpfit$dnode[, -(1:3), drop = FALSE]
## if (is.null(init$summary))
## stop("Initialization routine is missing the 'summary' function")
## functions <- if (is.null(init$print))
## list(summary = init$summary)
## else list(summary = init$summary, print = init$print)
## if (!is.null(init$text))
## functions <- c(functions, list(text = init$text))
## if (method == "user")
## functions <- c(functions, mlist)
## where <- rpfit$which
## names(where) <- row.names(m)
## ans <- list(frame = frame, where = where, call = Call, terms = Terms,
## cptable = t(rpfit$cptable), method = method, parms = init$parms,
## control = controls, functions = functions, numresp = init$numresp)
## if (nsplit)
## ans$splits = splits
## if (ncat > 0)
## ans$csplit <- catmat + 2
## if (nsplit)
## ans$variable.importance <- importance(ans)
## if (model) {
## ans$model <- m
## if (missing(y))
## y <- FALSE
## }
## if (y)
## ans$y <- Y
## if (x) {
## ans$x <- X
## ans$wt <- wt
## }
## ans$ordered <- isord
## if (!is.null(attr(m, "na.action")))
## ans$na.action <- attr(m, "na.action")
## if (!is.null(xlevels))
## attr(ans, "xlevels") <- xlevels
## if (method == "class")
## attr(ans, "ylevels") <- init$ylevels
## class(ans) <- "rpart"
## ans
## })(formula = .outcome ~ ., data = list(c(33, 37, 37, 9, 40, 23,
## 39, 33, 33, 11, 10, 9, 33, 41, 23, 33, 38, 22, 13, 31, 33, 33,
## 13, 34, 13, 33, 37, 40, 31, 33, 24, 23, 33, 38, 13, 8, 7, 41,
## 39, 33, 24, 11, 8, 33, 3, 38, 36, 38, 39, 33, 33, 25, 20, 11,
## 33, 39, 11, 12, 35, 30, 30, 36, 34, 23, 11, 33, 36, 13, 36, 29,
## 9, 25, 32, 8, 11, 3, 38, 11, 3, 13, 3, 3, 1, 41, 23, 38, 1, 39,
## 36, 38, 9, 8, 3, 26, 39, 11, 39, 9, 36, 24, 33, 1, 33, 11, 37,
## 24, 2, 23, 37, 36, 8, 23, 33, 34, 33, 22, 34, 33, 8, 33, 37,
## 35, 34, 9, 10, 30, 36, 3, 25, 23, 8, 37, 38, 8, 7, 29, 33, 33,
## 1, 13, 26, 13, 34, 38, 33, 33, 31, 8, 40, 8, 8, 3, 38, 12, 10,
## 37, 10, 35, 32, 39, 24, 9, 31, 40, 41, 39, 38, 37, 35, 9, 9,
## 11, 41, 33, 34, 29, 9, 8, 33, 41, 10, 9, 10, 3, 33, 25, 38, 38,
## 41, 13, 33, 33, 31, 2, 36, 39, 9, 39, 35, 33, 22, 35, 10, 38,
## 12, 9, 24, 11, 33, 9, 22, 38, 37, 36, 33, 40, 33, 10, 13, 35,
## 31, 22, 33, 29, 24, 37, 10, 11, 37, 36, 4, 8, 36, 31, 38, 8,
## 31, 39, 35, 8, 8, 10, 40, 35, 39, 38, 1, 33, 33, 38, 39, 2, 16,
## 38, 36, 39, 23, 32, 37, 33, 11, 10, 4, 2, 22, 9, 5, 26, 10, 9,
## 36, 33, 38, 25, 1, 33, 23, 24, 22, 9, 30, 8, 3, 36, 41, 41, 11,
## 3, 33, 9, 34, 41, 21, 3, 2, 23, 30, 8, 32, 9, 33, 8, 39, 33,
## 33, 36, 33, 35, 1, 13, 33, 16, 39, 13, 3, 13, 33, 1, 35, 8, 41,
## 33, 33, 10, 33, 35, 8, 32, 39, 22, 33, 29, 41, 37, 16, 12, 38,
## 33, 41, 6, 10, 31, 33, 24, 37, 41, 34, 1, 35, 12, 41, 36, 6,
## 39, 23, 9, 8, 34, 8, 34, 33, 4, 41, 38, 34, 32, 32, 12, 9, 33,
## 8, 31, 2, 37, 9, 8, 39, 32, 26, 35, 35, 33, 34, 33, 34, 18, 13,
## 33, 37, 6, 13, 35, 34, 33, 2, 8, 41, 33, 24, 33, 31, 36, 41,
## 34, 36, 33, 11, 4, 34, 4, 38, 38, 2, 1, 38, 8, 2, 8, 22, 12,
## 30, 30, 6, 4, 10, 21, 38, 12, 23, 3, 33, 33, 27, 30, 38, 36,
## 9, 36, 22, 6, 6, 9, 1, 27, 33, 36, 9, 7, 38, 33, 22, 8, 16, 38,
## 1, 35, 23, 38, 20, 28, 3, 35, 35, 29, 9, 36, 33, 23, 8, 33, 9,
## 33, 38, 33, 33, 35, 8, 24, 27, 26, 32, 4, 8, 33, 24, 9, 30, 33,
## 3, 33, 40, 6, 27, 8, 24, 24, 8, 11, 5, 33, 24, 33, 33, 33, 12,
## 39, 38, 36, 33, 40, 8, 3, 33, 32, 13, 39, 33, 36, 23, 35, 39,
## 25, 11, 22, 35, 39, 6, 31, 38, 31, 32, 5, 24, 39, 3, 33, 22,
## 34, 1, 6, 35, 33, 41, 36, 25, 38, 39, 33, 25, 1, 39, 36, 3, 33,
## 38, 33, 41, 23, 29, 2, 8, 23, 23, 9, 24, 7, 3, 33, 33, 30, 34,
## 38, 24, 23, 1, 9, 1, 36, 33, 26, 5, 1, 2, 3, 16, 7, 38, 39, 38,
## 36, 32, 2, 38, 31, 1, 13, 34, 10, 33, 38, 10, 40, 41, 35, 24,
## 8, 38, 33, 10, 39, 36, 34, 12, 34, 39, 41, 38, 38, 39, 3, 39,
## 37, 32, 41, 9, 33, 33, 31, 31, 34, 34, 39, 9, 33, 3, 26, 9, 12,
## 13, 22, 10, 36, 22, 31, 30, 13, 9, 40, 6, 33, 3, 24, 33, 32,
## 33, 28, 37, 39, 33, 33, 24, 8, 38, 7, 38, 28, 8, 1, 31, 38, 24,
## 1, 33, 6, 3, 11, 33, 36, 8, 27, 1, 39, 12, 31, 8, 41, 13, 22,
## 39, 30, 33, 24, 24, 39, 35, 12, 4, 31, 33, 13, 27, 36, 12, 8,
## 33, 13, 30, 33, 7, 31, 39, 31, 33, 38, 31, 1, 36, 13, 33, 33,
## 39, 29, 31, 29, 35, 33, 33, 20, 8, 29, 25, 3, 24, 32, 32, 31,
## 38, 31, 6, 10, 25, 10, 32, 37, 8, 31, 34, 2, 25, 33, 33, 24,
## 33, 23, 30, 38, 23, 38, 5, 31, 34, 24, 32, 39, 35, 33, 2, 8,
## 9, 33, 33, 33, 13, 38, 23, 33, 36, 11, 11, 38, 35, 8, 23, 11,
## 1, 3, 13, 23, 4, 37, 31, 38, 23, 21, 31, 33, 33, 8, 18, 1, 8,
## 38, 39, 10, 8, 12, 30, 32, 31, 9, 1, 3, 40, 33, 8, 8, 37, 3,
## 35, 10, 37, 38, 38, 38, 31, 2, 37, 3, 38, 33, 36, 39, 39, 9,
## 12, 33, 38, 3, 41, 36, 27, 8, 12, 22, 1, 20, 8, 37, 38, 33, 23,
## 38, 29, 38, 17, 11, 8, 34, 23, 11, 34, 24, 6, 10, 23, 2, 8, 22,
## 3, 33, 6, 33, 36, 32, 36, 6, 8, 38, 8, 39, 30, 38, 38, 38, 33,
## 9, 27, 2, 3, 32, 33, 39, 36, 35, 33, 6, 1, 32, 23, 1, 41, 31,
## 39, 10, 23, 23, 10, 33, 24, 13, 33, 6, 36, 32, 3, 28, 9, 36,
## 40, 3, 33, 36, 35, 39, 11, 36, 32, 8, 11, 6, 33, 25, 38, 38,
## 34, 36, 30, 29, 23, 5, 31, 13, 39, 33, 11, 33, 3, 35, 39, 32,
## 24, 5, 33, 39, 34, 31, 24, 33, 6, 2, 23, 39, 10, 33, 23, 33,
## 33, 40, 11, 36, 22, 36, 8, 30, 8, 36, 30, 32, 13, 33, 3, 1, 31,
## 38, 1, 7, 38, 5, 37, 38, 38, 38, 38, 40, 27, 33, 1, 33, 3, 33
## ), c(1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1,
## 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1,
## 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2,
## 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 3,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1,
## 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 10, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1,
## 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1), c(3, 2, 2, 3,
## 4, 2, 3, 2, 2, 3, 4, 3, 2, 3, 1, 2, 2, 3, 4, 2, 4, 3, 3, 3, 4,
## 3, 3, 3, 4, 2, 2, 2, 4, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3,
## 2, 4, 3, 3, 2, 2, 2, 2, 3, 5, 1, 3, 2, 3, 2, 3, 3, 1, 1, 4, 3,
## 3, 3, 2, 3, 2, 3, 3, 3, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 4,
## 1, 2, 3, 5, 3, 1, 2, 3, 2, 2, 2, 2, 3, 3, 4, 2, 3, 2, 4, 2, 2,
## 4, 4, 2, 2, 4, 3, 2, 2, 3, 2, 3, 3, 4, 3, 3, 3, 2, 2, 2, 2, 2,
## 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 1, 3, 4, 4, 3, 4, 3, 3, 5, 3, 4,
## 2, 3, 3, 4, 2, 4, 3, 2, 3, 2, 3, 3, 4, 3, 2, 3, 2, 4, 4, 2, 2,
## 2, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 2, 3, 1, 4, 3, 3, 3, 2, 3, 2,
## 2, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 4, 3, 3, 2, 2, 3, 2, 3, 3, 2,
## 2, 3, 2, 4, 3, 3, 2, 1, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3,
## 3, 3, 2, 3, 4, 3, 3, 3, 2, 5, 2, 4, 3, 2, 4, 3, 3, 2, 3, 2, 3,
## 1, 2, 2, 3, 2, 3, 1, 2, 2, 3, 3, 2, 3, 3, 2, 4, 2, 2, 2, 2, 2,
## 2, 1, 2, 2, 2, 1, 1, 3, 3, 3, 1, 2, 3, 3, 2, 3, 2, 4, 2, 2, 3,
## 1, 3, 4, 3, 3, 3, 3, 2, 3, 4, 2, 3, 2, 2, 3, 3, 2, 4, 4, 3, 2,
## 3, 2, 3, 3, 3, 2, 3, 4, 2, 3, 2, 3, 2, 3, 4, 2, 4, 4, 3, 3, 3,
## 3, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 4, 2, 1, 3, 4, 2, 3, 2, 3,
## 2, 3, 2, 3, 1, 2, 3, 3, 3, 3, 2, 4, 2, 4, 4, 3, 3, 2, 2, 4, 4,
## 3, 2, 3, 2, 3, 3, 2, 4, 3, 3, 1, 3, 3, 3, 3, 3, 2, 4, 3, 2, 4,
## 3, 3, 3, 3, 2, 3, 2, 2, 4, 2, 3, 2, 4, 4, 3, 2, 3, 1, 2, 3, 2,
## 4, 2, 3, 4, 1, 2, 3, 3, 2, 2, 4, 2, 2, 3, 2, 3, 3, 2, 4, 2, 3,
## 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 2, 1, 3, 2, 2, 3, 3, 3, 2, 2, 3,
## 3, 1, 4, 4, 3, 2, 4, 2, 3, 2, 4, 2, 2, 1, 2, 2, 4, 3, 2, 3, 2,
## 3, 1, 2, 3, 3, 2, 3, 3, 3, 4, 2, 2, 3, 4, 3, 3, 4, 3, 2, 3, 3,
## 2, 3, 3, 2, 3, 3, 3, 3, 3, 1, 1, 2, 3, 1, 3, 3, 2, 4, 3, 2, 3,
## 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 3, 1, 3, 4, 4, 2, 3,
## 2, 3, 1, 3, 4, 3, 3, 1, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2,
## 2, 2, 1, 4, 3, 3, 2, 2, 1, 2, 5, 3, 1, 1, 3, 2, 2, 3, 2, 3, 4,
## 2, 2, 3, 2, 3, 4, 3, 3, 3, 5, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4,
## 3, 3, 3, 3, 3, 5, 3, 2, 3, 2, 3, 2, 3, 3, 3, 4, 4, 3, 3, 2, 2,
## 2, 1, 4, 3, 3, 2, 3, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3,
## 2, 3, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 4, 3, 2, 2, 2, 3, 4, 2, 2,
## 3, 1, 3, 2, 3, 2, 3, 3, 3, 3, 4, 2, 3, 3, 2, 2, 2, 2, 3, 3, 2,
## 2, 3, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 2, 2, 4, 3, 2, 3, 3, 3,
## 3, 2, 2, 2, 2, 2, 3, 2, 4, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3, 3, 3,
## 3, 2, 3, 2, 2, 2, 3, 4, 4, 2, 4, 4, 2, 2, 2, 2, 4, 2, 2, 2, 4,
## 3, 2, 3, 4, 2, 4, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 2, 2, 4, 3, 3,
## 3, 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 1, 3, 3, 2, 2, 3, 4,
## 2, 3, 4, 4, 2, 2, 3, 3, 2, 2, 4, 2, 3, 3, 2, 2, 4, 3, 3, 2, 4,
## 2, 2, 3, 3, 2, 4, 4, 2, 5, 3, 3, 4, 3, 3, 2, 3, 2, 1, 3, 3, 2,
## 3, 3, 3, 3, 3, 3, 2, 2, 4, 3, 2, 1, 3, 3, 3, 3, 4, 2, 3, 4, 1,
## 2, 3, 1, 2, 2, 2, 3, 2, 2, 3, 3, 2, 4, 2, 2, 3, 4, 2, 3, 2, 3,
## 2, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 1, 3, 4, 3, 3, 3, 1, 2, 3,
## 3, 2, 3, 3, 3, 3, 3, 1, 2, 3, 2, 4, 2, 2, 2, 4, 3, 4, 2, 3, 2,
## 2, 3, 2, 2, 3, 4, 2, 3, 3, 3, 1, 2, 2, 2, 3, 2, 3, 3, 5, 2, 2,
## 3, 2, 3, 4, 5, 3, 2, 2, 2, 3, 3, 2, 3, 3, 2, 1, 3, 3, 3, 2, 2,
## 2, 4, 3, 2, 2, 2, 2, 1, 3, 2, 2, 3, 2, 3, 2, 3, 3, 2, 3, 4, 3,
## 3, 4, 2, 2, 2, 2, 3, 2, 2), c(2, 2, 2, 3, 2, 1, 2, 3, 4, 3, 3,
## 3, 3, 3, 2, 3, 3, 3, 2, 4, 3, 3, 2, 2, 3, 3, 3, 3, 2, 3, 2, 2,
## 3, 3, 3, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 3, 4, 2, 3, 3, 4, 3, 3,
## 4, 3, 2, 2, 2, 3, 3, 4, 3, 3, 1, 3, 2, 3, 3, 4, 5, 2, 5, 4, 3,
## 2, 4, 3, 3, 3, 3, 3, 4, 3, 3, 1, 3, 3, 2, 2, 2, 3, 3, 3, 5, 3,
## 3, 3, 3, 4, 2, 2, 4, 2, 5, 3, 2, 2, 2, 2, 3, 3, 1, 3, 3, 3, 4,
## 3, 3, 4, 3, 3, 3, 2, 3, 3, 4, 5, 4, 3, 2, 3, 3, 3, 3, 2, 3, 3,
## 3, 3, 2, 5, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 4, 3, 2, 2, 3, 3, 3,
## 4, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 2, 3, 5, 4, 3, 2, 4, 3, 3, 2,
## 3, 2, 2, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 2, 3, 4,
## 2, 4, 3, 2, 2, 3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3,
## 2, 3, 3, 4, 3, 3, 3, 4, 5, 4, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3,
## 3, 4, 2, 1, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 1, 3, 4, 3, 3, 2, 3,
## 4, 3, 2, 3, 4, 3, 2, 4, 2, 4, 3, 4, 3, 3, 3, 2, 3, 4, 4, 5, 4,
## 2, 3, 2, 4, 4, 3, 2, 3, 2, 4, 2, 2, 4, 3, 6, 3, 3, 3, 3, 3, 3,
## 3, 3, 3, 4, 3, 4, 2, 3, 3, 4, 2, 2, 3, 3, 2, 3, 3, 3, 2, 4, 3,
## 3, 4, 2, 2, 3, 1, 2, 3, 1, 2, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 2,
## 3, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 4, 2, 4, 2, 3, 3, 4, 5, 2,
## 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 4, 4, 3, 2, 2, 3, 3, 3, 3, 3, 4,
## 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 2, 3, 4, 2, 2, 3, 3, 3, 4, 3, 4,
## 3, 2, 3, 3, 4, 3, 2, 3, 2, 2, 5, 4, 3, 3, 2, 4, 2, 2, 3, 3, 3,
## 3, 4, 4, 3, 4, 2, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 2, 3, 2, 3, 3,
## 1, 3, 4, 2, 2, 2, 3, 4, 3, 3, 2, 1, 4, 3, 4, 3, 3, 2, 2, 2, 2,
## 3, 3, 4, 3, 2, 5, 6, 3, 3, 2, 3, 3, 2, 4, 4, 5, 4, 4, 3, 5, 3,
## 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 2, 2, 4, 3, 2, 3, 4, 3, 3, 3,
## 3, 2, 3, 3, 4, 2, 4, 3, 2, 4, 3, 3, 3, 3, 2, 3, 3, 2, 3, 4, 3,
## 4, 2, 4, 2, 4, 2, 3, 3, 5, 4, 3, 2, 3, 4, 3, 3, 2, 3, 2, 3, 2,
## 2, 3, 3, 3, 2, 2, 4, 2, 2, 3, 3, 2, 3, 3, 2, 2, 4, 3, 3, 4, 4,
## 3, 5, 4, 3, 3, 4, 1, 2, 3, 2, 3, 5, 3, 2, 2, 4, 4, 2, 2, 3, 2,
## 3, 3, 3, 3, 4, 2, 2, 3, 3, 2, 3, 4, 2, 2, 3, 3, 3, 3, 3, 2, 4,
## 2, 3, 4, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 5, 6, 3, 2, 3, 2, 2,
## 3, 3, 4, 4, 3, 3, 2, 2, 3, 4, 3, 3, 4, 3, 5, 3, 3, 4, 4, 4, 3,
## 3, 5, 3, 4, 3, 2, 3, 2, 2, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3,
## 3, 3, 3, 2, 3, 3, 2, 2, 3, 2, 4, 3, 3, 4, 3, 3, 2, 4, 3, 2, 3,
## 3, 2, 4, 3, 2, 3, 2, 4, 2, 2, 3, 4, 3, 2, 3, 3, 2, 3, 4, 3, 3,
## 3, 2, 2, 3, 4, 4, 4, 2, 4, 3, 3, 3, 3, 3, 3, 5, 3, 3, 5, 3, 4,
## 3, 2, 5, 2, 2, 3, 3, 3, 4, 2, 2, 2, 4, 3, 2, 3, 3, 2, 4, 3, 3,
## 3, 2, 3, 3, 3, 3, 2, 2, 3, 4, 5, 2, 3, 4, 4, 2, 3, 3, 4, 2, 2,
## 4, 2, 3, 3, 2, 4, 4, 6, 3, 2, 2, 4, 2, 2, 5, 4, 3, 2, 3, 4, 2,
## 3, 4, 3, 3, 2, 3, 3, 5, 4, 4, 3, 3, 3, 3, 2, 4, 4, 3, 3, 3, 2,
## 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 5, 2, 2, 2, 4, 3, 3, 3, 3, 3, 3,
## 2, 3, 3, 4, 2, 3, 2, 2, 2, 3, 3, 2, 3, 1, 4, 2, 2, 5, 3, 4, 3,
## 3, 4, 4, 3, 2, 2, 4, 4, 3, 2, 3, 4, 4, 3, 5, 3, 3, 3, 3, 3, 2,
## 3, 3, 2, 3, 3, 1, 4, 2, 3, 3, 3, 2, 3, 3, 2, 4, 2, 3, 2, 3, 3,
## 2, 4, 3, 4, 3, 3, 4, 2, 3, 3, 2, 2, 3, 4, 3, 3, 3, 4, 3, 2, 3,
## 4, 4, 4, 2, 3, 3, 2, 3, 3, 3, 3, 3, 4, 5, 3, 3, 3, 2, 3, 2, 3,
## 2, 4, 3, 3, 3, 3, 3, 4, 2, 4, 2, 2, 3, 4, 2, 3, 2, 3, 3, 4, 4,
## 4, 2, 3, 4, 3, 3, 2, 4, 2, 3, 4, 3, 2, 3, 3, 2, 4, 4, 4, 4, 3,
## 4, 4), c(8, 8, 8, 3, 10, 5, 9, 8, 8, 3, 3, 3, 8, 10, 5, 8, 9,
## 5, 3, 7, 8, 8, 3, 8, 3, 8, 8, 10, 7, 8, 5, 5, 8, 9, 3, 2, 2,
## 10, 9, 8, 5, 3, 2, 8, 1, 9, 8, 9, 9, 8, 8, 6, 5, 3, 8, 9, 3,
## 3, 8, 7, 7, 8, 8, 5, 3, 8, 8, 3, 8, 7, 3, 6, 7, 2, 3, 1, 9, 3,
## 1, 3, 1, 1, 1, 10, 5, 9, 1, 9, 8, 9, 3, 2, 1, 6, 9, 3, 9, 3,
## 8, 5, 8, 1, 8, 3, 8, 5, 1, 5, 8, 8, 2, 5, 8, 8, 8, 5, 8, 8, 2,
## 8, 8, 8, 8, 3, 3, 7, 8, 1, 6, 5, 2, 8, 9, 2, 2, 7, 8, 8, 1, 3,
## 6, 3, 8, 9, 8, 8, 7, 2, 10, 2, 2, 1, 9, 3, 3, 8, 3, 8, 7, 9,
## 5, 3, 7, 10, 10, 9, 9, 8, 8, 3, 3, 3, 10, 8, 8, 7, 3, 2, 8, 10,
## 3, 3, 3, 1, 8, 6, 9, 9, 10, 3, 8, 8, 7, 1, 8, 9, 3, 9, 8, 8,
## 5, 8, 3, 9, 3, 3, 5, 3, 8, 3, 5, 9, 8, 8, 8, 10, 8, 3, 3, 8,
## 7, 5, 8, 7, 5, 8, 3, 3, 8, 8, 1, 2, 8, 7, 9, 2, 7, 9, 8, 2, 2,
## 3, 10, 8, 9, 9, 1, 8, 8, 9, 9, 1, 4, 9, 8, 9, 5, 7, 8, 8, 3,
## 3, 1, 1, 5, 3, 1, 6, 3, 3, 8, 8, 9, 6, 1, 8, 5, 5, 5, 3, 7, 2,
## 1, 8, 10, 10, 3, 1, 8, 3, 8, 10, 5, 1, 1, 5, 7, 2, 7, 3, 8, 2,
## 9, 8, 8, 8, 8, 8, 1, 3, 8, 4, 9, 3, 1, 3, 8, 1, 8, 2, 10, 8,
## 8, 3, 8, 8, 2, 7, 9, 5, 8, 7, 10, 8, 4, 3, 9, 8, 10, 2, 3, 7,
## 8, 5, 8, 10, 8, 1, 8, 3, 10, 8, 2, 9, 5, 3, 2, 8, 2, 8, 8, 1,
## 10, 9, 8, 7, 7, 3, 3, 8, 2, 7, 1, 8, 3, 2, 9, 7, 6, 8, 8, 8,
## 8, 8, 8, 4, 3, 8, 8, 2, 3, 8, 8, 8, 1, 2, 10, 8, 5, 8, 7, 8,
## 10, 8, 8, 8, 3, 1, 8, 1, 9, 9, 1, 1, 9, 2, 1, 2, 5, 3, 7, 7,
## 2, 1, 3, 5, 9, 3, 5, 1, 8, 8, 6, 7, 9, 8, 3, 8, 5, 2, 2, 3, 1,
## 6, 8, 8, 3, 2, 9, 8, 5, 2, 4, 9, 1, 8, 5, 9, 5, 6, 1, 8, 8, 7,
## 3, 8, 8, 5, 2, 8, 3, 8, 9, 8, 8, 8, 2, 5, 6, 6, 7, 1, 2, 8, 5,
## 3, 7, 8, 1, 8, 10, 2, 6, 2, 5, 5, 2, 3, 1, 8, 5, 8, 8, 8, 3,
## 9, 9, 8, 8, 10, 2, 1, 8, 7, 3, 9, 8, 8, 5, 8, 9, 6, 3, 5, 8,
## 9, 2, 7, 9, 7, 7, 1, 5, 9, 1, 8, 5, 8, 1, 2, 8, 8, 10, 8, 6,
## 9, 9, 8, 6, 1, 9, 8, 1, 8, 9, 8, 10, 5, 7, 1, 2, 5, 5, 3, 5,
## 2, 1, 8, 8, 7, 8, 9, 5, 5, 1, 3, 1, 8, 8, 6, 1, 1, 1, 1, 4, 2,
## 9, 9, 9, 8, 7, 1, 9, 7, 1, 3, 8, 3, 8, 9, 3, 10, 10, 8, 5, 2,
## 9, 8, 3, 9, 8, 8, 3, 8, 9, 10, 9, 9, 9, 1, 9, 8, 7, 10, 3, 8,
## 8, 7, 7, 8, 8, 9, 3, 8, 1, 6, 3, 3, 3, 5, 3, 8, 5, 7, 7, 3, 3,
## 10, 2, 8, 1, 5, 8, 7, 8, 6, 8, 9, 8, 8, 5, 2, 9, 2, 9, 6, 2,
## 1, 7, 9, 5, 1, 8, 2, 1, 3, 8, 8, 2, 6, 1, 9, 3, 7, 2, 10, 3,
## 5, 9, 7, 8, 5, 5, 9, 8, 3, 1, 7, 8, 3, 6, 8, 3, 2, 8, 3, 7, 8,
## 2, 7, 9, 7, 8, 9, 7, 1, 8, 3, 8, 8, 9, 7, 7, 7, 8, 8, 8, 5, 2,
## 7, 6, 1, 5, 7, 7, 7, 9, 7, 2, 3, 6, 3, 7, 8, 2, 7, 8, 1, 6, 8,
## 8, 5, 8, 5, 7, 9, 5, 9, 1, 7, 8, 5, 7, 9, 8, 8, 1, 2, 3, 8, 8,
## 8, 3, 9, 5, 8, 8, 3, 3, 9, 8, 2, 5, 3, 1, 1, 3, 5, 1, 8, 7, 9,
## 5, 5, 7, 8, 8, 2, 4, 1, 2, 9, 9, 3, 2, 3, 7, 7, 7, 3, 1, 1, 10,
## 8, 2, 2, 8, 1, 8, 3, 8, 9, 9, 9, 7, 1, 8, 1, 9, 8, 8, 9, 9, 3,
## 3, 8, 9, 1, 10, 8, 6, 2, 3, 5, 1, 5, 2, 8, 9, 8, 5, 9, 7, 9,
## 4, 3, 2, 8, 5, 3, 8, 5, 2, 3, 5, 1, 2, 5, 1, 8, 2, 8, 8, 7, 8,
## 2, 2, 9, 2, 9, 7, 9, 9, 9, 8, 3, 6, 1, 1, 7, 8, 9, 8, 8, 8, 2,
## 1, 7, 5, 1, 10, 7, 9, 3, 5, 5, 3, 8, 5, 3, 8, 2, 8, 7, 1, 6,
## 3, 8, 10, 1, 8, 8, 8, 9, 3, 8, 7, 2, 3, 2, 8, 6, 9, 9, 8, 8,
## 7, 7, 5, 1, 7, 3, 9, 8, 3, 8, 1, 8, 9, 7, 5, 1, 8, 9, 8, 7, 5,
## 8, 2, 1, 5, 9, 3, 8, 5, 8, 8, 10, 3, 8, 5, 8, 2, 7, 2, 8, 7,
## 7, 3, 8, 1, 1, 7, 9, 1, 2, 9, 1, 8, 9, 9, 9, 9, 10, 6, 8, 1,
## 8, 1, 8), c(0, 1, 0, 2, 1, 0, 2, 0, 0, 3, 1, 1, 1, 0, 0, 0, 0,
## 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 2, 0, 0,
## 0, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,
## 0, 0, 1, 0, 0, 4, 0, 0, 0, 4, 2, 0, 1, 1, 0, 1, 0, 0, 0, 3, 1,
## 0, 1, 6, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0,
## 0, 0, 2, 2, 0, 1, 3, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0, 1, 0, 3, 1,
## 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 0, 1, 1, 0, 1, 4, 1, 1, 0,
## 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 5, 0, 0, 2, 0, 2, 2, 1,
## 0, 0, 1, 9, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 0, 1, 0, 0, 0, 1,
## 3, 0, 1, 1, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 1,
## 1, 1, 0, 1, 0, 0, 2, 1, 0, 0, 3, 5, 0, 1, 0, 0, 0, 1, 1, 0, 0,
## 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 1, 0,
## 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 9, 1, 0, 0, 5, 0, 1, 0, 1, 0, 2,
## 0, 1, 0, 1, 0, 1, 0, 2, 3, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0,
## 0, 1, 3, 0, 1, 2, 1, 1, 0, 1, 0, 2, 1, 0, 1, 0, 0, 1, 0, 3, 0,
## 1, 1, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2,
## 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 3, 0, 4,
## 0, 1, 3, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0,
## 2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 4, 2, 0, 2, 2, 0, 0, 1, 1, 0,
## 2, 0, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 0, 1, 0, 1, 0, 9, 1, 1, 1,
## 0, 3, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0,
## 1, 2, 0, 3, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 1, 0,
## 1, 1, 2, 1, 0, 2, 1, 0, 0, 1, 1, 0, 0, 0, 0, 4, 1, 0, 0, 0, 1,
## 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1,
## 0, 0, 0, 0, 1, 0, 0, 4, 0, 1, 2, 0, 0, 0, 2, 1, 0, 1, 1, 2, 0,
## 0, 1, 1, 0, 0, 0, 3, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 2, 0, 0, 4, 2, 0, 1, 0, 1, 0, 0, 2, 1, 1, 1, 2, 0, 0,
## 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1,
## 4, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0,
## 2, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0,
## 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 1, 0, 0, 2, 0, 1,
## 0, 2, 2, 0, 3, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 3,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 0, 1, 1, 0, 1, 0,
## 0, 0, 2, 1, 3, 0, 0, 2, 0, 1, 0, 0, 1, 4, 0, 1, 1, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 4, 0, 4, 3, 0, 1, 1, 1, 2,
## 2, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 1, 1, 0, 0, 1,
## 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 1, 0, 1,
## 0, 2, 0, 0, 2, 0, 1, 0, 0, 2, 1, 1, 1, 1, 2, 0, 0, 0, 1, 0, 6,
## 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 0, 1, 2, 0, 0,
## 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
## 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1,
## 0, 2, 0, 0, 0, 1, 5, 0, 0, 2, 0, 1, 1, 1, 0, 1, 2, 1, 2, 0, 1,
## 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 0, 3, 0, 0,
## 0, 1, 1, 1, 1, 2, 1, 0, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 0, 1, 1,
## 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0,
## 0, 1, 0, 1, 0, 1, 2, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0,
## 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 2, 1,
## 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0), c(5, 4, 4,
## 3, 4, 5, 2, 7, 1, 5, 4, 3, 4, 5, 6, 7, 6, 5, 4, 2, 6, 4, 7, 7,
## 4, 6, 5, 3, 9, 7, 3, 4, 4, 5, 4, 4, 7, 7, 6, 2, 5, 7, 4, 5, 7,
## 5, 5, 4, 4, 4, 2, 5, 4, 7, 6, 5, 5, 6, 4, 4, 5, 4, 4, 2, 0, 8,
## 6, 6, 3, 2, 5, 5, 5, 5, 4, 5, 4, 6, 3, 4, 6, 4, 0, 6, 2, 5, 7,
## 0, 6, 4, 4, 5, 6, 4, 7, 8, 4, 6, 4, 4, 4, 6, 8, 4, 6, 3, 4, 3,
## 4, 4, 5, 5, 7, 4, 7, 2, 5, 2, 4, 9, 3, 4, 7, 5, 3, 4, 5, 4, 5,
## 4, 5, 5, 1, 6, 0, 6, 4, 5, 7, 0, 4, 5, 2, 4, 1, 5, 2, 3, 1, 5,
## 5, 4, 3, 3, 5, 4, 3, 6, 4, 4, 4, 3, 2, 4, 5, 4, 4, 0, 4, 6, 4,
## 4, 5, 6, 7, 4, 2, 4, 6, 7, 2, 3, 5, 6, 4, 2, 2, 4, 4, 4, 7, 3,
## 2, 5, 7, 6, 5, 5, 5, 5, 3, 9, 4, 0, 7, 4, 4, 4, 6, 2, 6, 3, 4,
## 5, 7, 7, 6, 3, 7, 4, 0, 5, 6, 6, 4, 4, 9, 3, 5, 5, 5, 7, 1, 9,
## 6, 7, 2, 6, 4, 5, 4, 4, 3, 5, 5, 5, 5, 7, 7, 4, 5, 2, 3, 2, 5,
## 9, 5, 5, 0, 4, 0, 4, 3, 5, 5, 4, 3, 3, 4, 4, 6, 4, 3, 5, 6, 9,
## 4, 1, 5, 4, 4, 7, 5, 5, 9, 6, 5, 5, 5, 1, 7, 4, 4, 4, 4, 4, 4,
## 5, 5, 4, 6, 4, 4, 5, 5, 3, 9, 4, 2, 2, 7, 3, 5, 6, 4, 4, 6, 3,
## 5, 5, 9, 6, 6, 5, 5, 5, 4, 3, 8, 6, 4, 5, 5, 5, 1, 4, 2, 4, 7,
## 4, 5, 4, 5, 3, 6, 9, 7, 5, 4, 6, 2, 8, 0, 4, 4, 4, 5, 4, 5, 3,
## 7, 5, 9, 5, 4, 3, 9, 3, 4, 5, 4, 3, 4, 4, 4, 5, 6, 6, 3, 4, 4,
## 6, 7, 7, 3, 5, 4, 6, 3, 1, 2, 7, 4, 4, 6, 5, 6, 4, 5, 4, 3, 7,
## 4, 5, 5, 4, 7, 5, 4, 5, 5, 6, 0, 6, 5, 5, 0, 3, 8, 5, 6, 4, 5,
## 5, 2, 5, 6, 2, 6, 4, 7, 5, 5, 4, 1, 6, 4, 5, 4, 7, 5, 5, 5, 4,
## 4, 6, 5, 7, 9, 3, 9, 4, 4, 5, 5, 5, 4, 6, 4, 6, 4, 7, 3, 5, 5,
## 7, 7, 4, 5, 6, 3, 4, 4, 4, 4, 2, 7, 4, 5, 5, 5, 5, 3, 5, 2, 4,
## 4, 4, 4, 4, 7, 2, 5, 3, 4, 4, 5, 4, 5, 5, 5, 3, 5, 6, 3, 5, 6,
## 3, 9, 3, 5, 5, 9, 6, 4, 5, 4, 6, 4, 4, 5, 9, 4, 3, 5, 6, 7, 5,
## 4, 3, 5, 5, 4, 5, 5, 3, 5, 7, 7, 7, 9, 4, 4, 6, 4, 2, 6, 6, 2,
## 2, 5, 3, 5, 4, 2, 7, 5, 4, 5, 5, 3, 1, 3, 4, 4, 7, 6, 7, 4, 5,
## 5, 4, 3, 2, 5, 6, 4, 6, 7, 4, 5, 5, 6, 5, 3, 7, 5, 5, 6, 4, 7,
## 4, 4, 6, 5, 9, 7, 4, 4, 4, 3, 1, 5, 2, 3, 2, 4, 5, 4, 9, 6, 5,
## 5, 4, 5, 7, 1, 3, 5, 6, 3, 6, 3, 7, 4, 7, 4, 4, 9, 4, 4, 4, 7,
## 7, 8, 5, 6, 1, 6, 8, 3, 5, 5, 6, 6, 6, 4, 6, 5, 7, 9, 1, 4, 5,
## 1, 7, 6, 5, 5, 5, 5, 5, 3, 8, 3, 7, 4, 3, 2, 4, 4, 4, 4, 6, 6,
## 4, 4, 6, 4, 9, 7, 6, 1, 5, 6, 4, 7, 3, 7, 2, 4, 3, 4, 5, 4, 6,
## 1, 4, 5, 7, 5, 4, 1, 4, 4, 5, 3, 7, 7, 5, 6, 6, 5, 3, 6, 2, 4,
## 7, 7, 7, 6, 5, 2, 3, 3, 4, 5, 5, 6, 3, 4, 7, 5, 6, 5, 5, 4, 2,
## 5, 4, 6, 3, 2, 3, 5, 8, 4, 4, 5, 8, 4, 6, 3, 5, 4, 6, 4, 5, 5,
## 3, 7, 7, 6, 0, 5, 4, 5, 6, 6, 6, 4, 6, 5, 4, 3, 4, 9, 4, 6, 4,
## 9, 6, 4, 5, 4, 6, 5, 4, 7, 4, 4, 5, 6, 1, 6, 5, 6, 8, 1, 2, 7,
## 2, 5, 2, 5, 4, 9, 3, 6, 0, 5, 5, 5, 3, 4, 7, 4, 5, 4, 6, 2, 3,
## 4, 5, 2, 4, 6, 6, 6, 6, 4, 6, 4, 5, 2, 3, 4, 5, 6, 5, 5, 4, 3,
## 4, 6, 4, 6, 7, 5, 1, 5, 5, 4, 3, 5, 5, 7, 7, 3, 5, 4, 6, 1, 3,
## 2, 5, 4, 5, 5, 4, 3, 4, 4, 6, 4, 4, 3, 4, 4, 2, 5, 4, 5, 7, 7,
## 5, 5, 6, 7, 6, 5, 4, 5, 5, 9, 7, 5, 5, 2, 5, 5, 4, 6, 4, 3, 4,
## 4, 4, 4, 7, 5, 5, 1, 5, 5, 6, 5, 7, 4, 5, 1, 4, 4, 6, 9, 5, 9,
## 4, 4, 6, 7, 5, 4, 2, 4, 6, 5, 4, 4, 5, 6, 9, 5, 7, 4, 3, 5, 5,
## 5, 4, 3, 3, 6, 6, 7, 6, 3, 2, 5, 6, 6, 7, 3, 5, 0, 4, 2, 6, 3,
## 9, 4, 4, 4, 6, 5, 5, 3, 3, 3, 7, 4, 5, 4, 6, 4, 7, 4, 5, 2, 4,
## 3, 6, 6, 6, 5, 5, 2, 5, 4, 9), c(1, 1, 2, 2, 1, 0, 0, 0, 3, 0,
## 1, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 1, 2,
## 2, 1, 2, 2, 1, 2, 1, 0, 3, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 2, 1,
## 2, 0, 1, 0, 1, 0, 4, 1, 3, 1, 0, 4, 0, 1, 1, 0, 0, 2, 0, 2, 1,
## 2, 0, 2, 2, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 1, 2, 1, 0, 1, 2,
## 2, 0, 0, 1, 2, 1, 0, 2, 1, 4, 1, 1, 1, 0, 2, 2, 1, 0, 0, 2, 1,
## 3, 2, 2, 2, 0, 0, 2, 0, 1, 0, 0, 2, 4, 1, 1, 2, 2, 2, 2, 0, 0,
## 2, 0, 0, 0, 1, 1, 0, 2, 3, 0, 3, 4, 5, 2, 1, 0, 3, 0, 1, 1, 1,
## 1, 2, 1, 2, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 4, 2, 1, 1, 0, 3, 1,
## 2, 0, 2, 0, 0, 0, 2, 1, 3, 1, 1, 2, 2, 4, 0, 1, 0, 1, 0, 1, 2,
## 0, 1, 0, 1, 1, 2, 1, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 1,
## 2, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 0, 0, 0, 0, 0, 3, 1, 0, 1, 1,
## 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 2, 0, 2, 2, 0, 1, 1, 0, 2, 0, 2,
## 0, 2, 0, 2, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 2, 1, 2, 1, 2, 0, 2,
## 2, 0, 0, 2, 0, 2, 3, 0, 1, 0, 0, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1,
## 1, 0, 0, 2, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 1, 1, 1, 0,
## 1, 1, 3, 0, 1, 0, 1, 1, 3, 0, 0, 3, 1, 1, 1, 0, 1, 0, 2, 1, 0,
## 0, 3, 2, 0, 1, 0, 5, 1, 1, 3, 0, 1, 2, 2, 0, 1, 0, 1, 0, 1, 0,
## 3, 1, 1, 4, 1, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 3, 0, 1, 1,
## 0, 0, 4, 0, 1, 2, 0, 2, 1, 1, 1, 0, 0, 0, 1, 1, 2, 2, 0, 1, 1,
## 2, 1, 0, 0, 0, 2, 1, 0, 1, 1, 1, 1, 2, 2, 2, 1, 1, 0, 0, 1, 0,
## 0, 1, 2, 2, 3, 0, 2, 2, 4, 2, 2, 3, 1, 2, 1, 0, 0, 2, 0, 1, 0,
## 1, 1, 1, 2, 0, 1, 0, 2, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 2, 0, 2,
## 0, 0, 2, 0, 0, 2, 3, 2, 1, 2, 3, 1, 2, 0, 1, 0, 1, 2, 0, 0, 3,
## 0, 1, 2, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 2, 2, 0, 0,
## 1, 1, 2, 1, 1, 2, 0, 0, 1, 3, 2, 1, 2, 0, 0, 2, 2, 0, 1, 1, 0,
## 3, 2, 0, 0, 2, 0, 0, 1, 1, 2, 2, 1, 0, 1, 2, 1, 1, 0, 1, 4, 0,
## 0, 1, 1, 1, 0, 3, 1, 4, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 0,
## 0, 2, 2, 2, 0, 1, 0, 0, 2, 1, 0, 2, 2, 1, 1, 1, 0, 1, 0, 0, 1,
## 0, 2, 0, 5, 2, 1, 1, 3, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 2, 0, 0,
## 1, 2, 1, 1, 0, 2, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1,
## 1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 1, 1, 3, 1, 1, 1, 2, 0, 1,
## 1, 2, 0, 0, 1, 1, 3, 3, 2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0,
## 2, 0, 2, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 5, 2, 1, 2, 2, 1, 0,
## 1, 1, 1, 0, 0, 2, 3, 1, 0, 1, 1, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0,
## 1, 0, 0, 1, 2, 1, 2, 0, 1, 1, 1, 1, 0, 3, 2, 2, 1, 0, 2, 2, 0,
## 0, 1, 1, 1, 1, 0, 1, 3, 1, 2, 0, 2, 1, 3, 0, 0, 0, 0, 2, 1, 1,
## 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 0, 4, 1, 1, 0, 0, 1, 3, 2, 1, 1,
## 1, 2, 2, 3, 1, 2, 0, 0, 1, 2, 0, 1, 0, 2, 3, 4, 4, 1, 2, 0, 3,
## 0, 0, 2, 4, 0, 2, 1, 0, 1, 0, 1, 0, 2, 3, 1, 2, 0, 0, 1, 1, 0,
## 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 1, 1, 2, 1, 3,
## 0, 1, 0, 0, 3, 1, 0, 0, 2, 0, 1, 1, 3, 1, 4, 0, 1, 2, 2, 1, 1,
## 0, 1, 0, 1, 1, 0, 1, 2, 4, 2, 0, 1, 0, 0, 2, 3, 1, 0, 1, 1, 2,
## 0, 2, 0, 2, 0, 1, 4, 2, 1, 1, 1, 1, 1, 2, 2, 0, 1, 0, 0, 0, 0,
## 1, 0, 1, 1, 2, 1, 4, 3, 2, 2, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 4,
## 1, 0, 1, 0, 1, 2, 0, 0, 0, 2, 2, 4, 2, 1, 4, 2, 1, 1, 0, 0, 0,
## 0, 1, 2, 2, 0, 1, 0, 0, 1, 0, 0, 4, 0, 0, 0, 2, 0, 1, 0, 0, 2,
## 0, 1, 2, 1, 2, 3, 2, 1, 0, 2, 0, 3, 2, 1, 0, 2, 0, 0, 2, 0, 0,
## 0, 2, 0), c(3, 4, 4, 4, 4, 5, 5, 2, 6, 2, 4, 4, 4, 4, 2, 2, 3,
## 4, 3, 7, 3, 3, 2, 2, 4, 2, 4, 6, 0, 2, 4, 4, 5, 2, 4, 4, 0, 2,
## 3, 5, 3, 0, 4, 4, 0, 3, 3, 5, 3, 5, 5, 4, 3, 2, 3, 3, 4, 3, 2,
## 4, 2, 4, 5, 4, 5, 0, 2, 3, 2, 4, 4, 2, 3, 3, 5, 2, 3, 2, 4, 5,
## 3, 4, 3, 2, 6, 3, 2, 5, 2, 4, 5, 4, 2, 4, 0, 1, 5, 2, 2, 2, 5,
## 2, 0, 0, 2, 6, 4, 4, 4, 3, 2, 5, 2, 3, 2, 4, 2, 6, 4, 0, 3, 3,
## 2, 4, 6, 5, 2, 2, 4, 3, 1, 3, 6, 2, 9, 3, 3, 4, 2, 5, 4, 3, 7,
## 4, 5, 4, 4, 2, 3, 3, 3, 5, 4, 5, 4, 4, 1, 3, 3, 3, 3, 4, 5, 4,
## 4, 5, 4, 0, 5, 3, 5, 0, 2, 3, 2, 4, 4, 4, 1, 3, 6, 6, 4, 3, 3,
## 4, 5, 5, 4, 4, 0, 3, 7, 3, 2, 2, 4, 3, 2, 3, 6, 0, 4, 7, 0, 5,
## 3, 5, 3, 7, 2, 6, 4, 3, 2, 2, 0, 1, 2, 5, 7, 2, 2, 3, 5, 4, 0,
## 5, 4, 2, 3, 2, 6, 0, 3, 1, 5, 3, 5, 2, 3, 5, 6, 2, 3, 2, 3, 2,
## 2, 4, 3, 5, 6, 4, 1, 0, 4, 3, 0, 3, 9, 4, 2, 2, 3, 4, 5, 6, 3,
## 5, 2, 5, 6, 3, 3, 0, 3, 5, 2, 4, 4, 2, 2, 2, 0, 3, 3, 3, 2, 5,
## 2, 4, 3, 5, 4, 3, 4, 3, 4, 5, 3, 3, 5, 4, 3, 6, 0, 3, 7, 4, 0,
## 6, 3, 3, 4, 3, 1, 5, 3, 3, 0, 2, 2, 3, 5, 3, 4, 4, 1, 2, 5, 2,
## 3, 1, 6, 5, 5, 5, 2, 3, 4, 5, 4, 4, 3, 0, 2, 0, 3, 3, 5, 1, 0,
## 5, 4, 1, 5, 4, 2, 5, 2, 3, 0, 3, 5, 5, 0, 3, 5, 3, 2, 5, 4, 4,
## 3, 5, 3, 3, 6, 5, 3, 1, 2, 2, 4, 0, 3, 3, 4, 6, 4, 2, 4, 3, 3,
## 1, 2, 5, 3, 5, 5, 2, 4, 4, 2, 3, 0, 4, 4, 3, 3, 3, 0, 3, 1, 3,
## 9, 4, 1, 3, 3, 3, 3, 2, 5, 3, 3, 7, 3, 5, 2, 3, 3, 4, 6, 2, 4,
## 2, 0, 0, 0, 2, 3, 3, 5, 3, 4, 0, 0, 5, 0, 3, 5, 3, 2, 4, 4, 3,
## 3, 3, 3, 2, 5, 2, 2, 2, 2, 4, 3, 1, 6, 4, 5, 2, 3, 7, 2, 4, 1,
## 2, 3, 2, 2, 3, 5, 5, 5, 5, 4, 4, 2, 7, 1, 6, 4, 3, 3, 4, 4, 3,
## 4, 6, 3, 3, 5, 4, 0, 2, 0, 5, 1, 3, 0, 3, 3, 3, 4, 2, 4, 2, 4,
## 0, 4, 4, 2, 3, 0, 2, 5, 5, 2, 4, 4, 3, 4, 4, 2, 2, 2, 0, 0, 5,
## 4, 2, 4, 4, 3, 3, 3, 5, 3, 5, 4, 5, 4, 2, 2, 4, 2, 3, 5, 6, 5,
## 2, 3, 0, 2, 2, 4, 3, 2, 5, 6, 4, 1, 2, 5, 2, 0, 4, 3, 4, 2, 3,
## 3, 0, 3, 4, 2, 3, 1, 4, 5, 2, 3, 0, 2, 4, 5, 3, 6, 3, 2, 5, 6,
## 3, 5, 4, 4, 0, 3, 4, 0, 5, 4, 2, 6, 6, 3, 3, 5, 2, 5, 3, 4, 2,
## 5, 5, 0, 3, 5, 4, 2, 2, 1, 4, 3, 5, 3, 1, 3, 3, 4, 3, 2, 3, 3,
## 3, 3, 0, 0, 5, 4, 3, 5, 1, 3, 4, 2, 4, 3, 3, 5, 1, 6, 2, 3, 2,
## 4, 4, 5, 5, 5, 3, 3, 5, 5, 2, 4, 0, 2, 3, 5, 4, 1, 4, 2, 5, 2,
## 7, 5, 5, 4, 1, 5, 3, 2, 4, 3, 0, 3, 4, 5, 4, 4, 3, 6, 2, 0, 2,
## 3, 3, 4, 5, 3, 5, 4, 2, 2, 2, 3, 2, 3, 6, 2, 3, 4, 4, 2, 5, 3,
## 0, 4, 3, 3, 3, 5, 4, 3, 4, 2, 6, 5, 4, 3, 1, 5, 4, 2, 0, 5, 2,
## 4, 4, 4, 3, 4, 4, 2, 6, 2, 2, 3, 5, 3, 4, 3, 3, 3, 2, 4, 1, 3,
## 5, 4, 5, 0, 0, 3, 4, 0, 3, 3, 2, 3, 2, 3, 3, 0, 4, 3, 3, 2, 2,
## 3, 2, 2, 1, 7, 7, 0, 5, 0, 4, 3, 2, 0, 4, 4, 7, 2, 0, 3, 4, 4,
## 1, 4, 4, 4, 3, 6, 4, 4, 3, 7, 5, 3, 3, 3, 3, 4, 3, 4, 4, 7, 6,
## 5, 3, 2, 4, 4, 3, 5, 4, 2, 5, 3, 0, 4, 5, 4, 4, 4, 6, 2, 4, 1,
## 2, 4, 4, 5, 3, 6, 1, 4, 5, 4, 2, 3, 4, 5, 5, 4, 1, 4, 3, 6, 4,
## 4, 4, 3, 5, 3, 2, 2, 1, 1, 2, 2, 2, 3, 3, 3, 2, 0, 0, 2, 3, 4,
## 2, 3, 5, 2, 4, 5, 4, 4, 5, 4, 2, 3, 3, 6, 3, 4, 3, 4, 0, 4, 0,
## 6, 4, 3, 2, 0, 4, 0, 5, 5, 3, 2, 1, 5, 4, 4, 3, 3, 4, 4, 2, 3,
## 0, 3, 0, 3, 3, 3, 2, 0, 3, 5, 4, 3, 3, 2, 3, 6, 5, 0, 3, 2, 2,
## 5, 4, 9, 5, 4, 3, 6, 0, 3, 5, 4, 3, 3, 2, 6, 5, 4, 2, 3, 0, 3,
## 2, 5, 0, 5, 2, 5, 4, 6, 2, 3, 3, 3, 3, 7, 3, 4, 0), c(7, 6, 3,
## 5, 7, 0, 7, 7, 6, 7, 7, 7, 6, 7, 1, 7, 7, 7, 7, 9, 9, 7, 7, 7,
## 8, 6, 7, 9, 5, 5, 2, 7, 8, 4, 8, 6, 7, 8, 6, 6, 6, 9, 6, 8, 7,
## 7, 6, 8, 8, 7, 7, 3, 6, 6, 7, 7, 4, 7, 7, 6, 4, 6, 9, 2, 0, 9,
## 7, 6, 6, 6, 9, 5, 8, 7, 6, 7, 5, 7, 8, 6, 5, 7, 8, 6, 4, 5, 8,
## 9, 1, 7, 7, 9, 6, 3, 9, 9, 9, 7, 7, 1, 9, 9, 9, 5, 7, 4, 7, 6,
## 3, 7, 6, 0, 7, 7, 8, 4, 6, 6, 5, 5, 7, 7, 7, 7, 9, 3, 5, 6, 3,
## 3, 7, 5, 5, 9, 5, 3, 7, 4, 8, 5, 3, 7, 7, 7, 7, 8, 6, 9, 9, 7,
## 7, 7, 6, 5, 8, 6, 8, 7, 5, 8, 5, 8, 6, 6, 7, 3, 7, 5, 6, 7, 4,
## 5, 7, 7, 8, 7, 7, 9, 6, 8, 9, 5, 9, 9, 7, 1, 6, 7, 7, 7, 9, 9,
## 9, 5, 7, 5, 7, 7, 6, 9, 6, 5, 9, 4, 9, 7, 6, 5, 6, 5, 1, 7, 7,
## 5, 7, 6, 5, 8, 8, 7, 8, 1, 6, 4, 6, 6, 7, 4, 6, 5, 6, 9, 8, 5,
## 5, 6, 6, 6, 5, 6, 6, 7, 9, 8, 7, 7, 6, 7, 7, 7, 7, 9, 2, 7, 6,
## 9, 2, 6, 5, 7, 5, 9, 6, 7, 4, 8, 5, 5, 6, 9, 7, 8, 7, 7, 5, 5,
## 2, 3, 1, 6, 6, 9, 5, 4, 9, 7, 8, 5, 6, 7, 7, 7, 4, 6, 7, 3, 6,
## 7, 3, 7, 9, 6, 6, 7, 7, 3, 5, 7, 6, 5, 5, 1, 7, 6, 5, 7, 6, 7,
## 5, 9, 5, 6, 6, 8, 9, 7, 7, 5, 8, 1, 9, 4, 6, 7, 1, 9, 6, 6, 8,
## 6, 7, 5, 7, 6, 8, 5, 7, 9, 7, 7, 7, 9, 5, 3, 2, 7, 9, 7, 7, 5,
## 7, 6, 9, 5, 9, 5, 9, 5, 7, 7, 5, 4, 7, 6, 7, 9, 6, 7, 5, 3, 7,
## 6, 7, 7, 6, 3, 6, 7, 4, 8, 7, 7, 7, 7, 8, 7, 6, 7, 4, 9, 4, 9,
## 7, 6, 5, 7, 9, 7, 7, 5, 5, 4, 9, 9, 6, 7, 4, 6, 2, 6, 1, 6, 7,
## 4, 7, 6, 6, 9, 2, 5, 5, 7, 7, 6, 9, 7, 4, 5, 5, 9, 7, 4, 6, 5,
## 7, 7, 7, 7, 5, 6, 5, 6, 1, 7, 9, 3, 2, 5, 6, 7, 6, 7, 8, 4, 6,
## 6, 6, 2, 7, 6, 5, 3, 8, 9, 7, 6, 9, 0, 7, 2, 6, 4, 9, 7, 5, 9,
## 3, 5, 7, 2, 6, 3, 7, 7, 6, 7, 7, 7, 5, 7, 8, 9, 7, 7, 7, 5, 9,
## 6, 9, 6, 7, 5, 9, 7, 6, 5, 8, 1, 2, 9, 7, 2, 6, 8, 7, 7, 9, 9,
## 9, 5, 6, 8, 2, 7, 5, 6, 9, 7, 7, 7, 9, 9, 7, 7, 3, 9, 7, 6, 5,
## 7, 7, 4, 0, 7, 7, 5, 9, 2, 6, 5, 7, 1, 3, 7, 4, 7, 5, 5, 8, 5,
## 6, 6, 5, 0, 8, 8, 7, 7, 9, 3, 5, 9, 6, 5, 2, 7, 5, 5, 7, 3, 7,
## 7, 6, 7, 6, 4, 7, 9, 9, 5, 9, 9, 5, 8, 4, 8, 9, 4, 7, 9, 7, 6,
## 9, 9, 5, 6, 5, 7, 7, 7, 5, 6, 5, 8, 4, 8, 7, 6, 5, 7, 9, 7, 7,
## 7, 7, 1, 9, 6, 6, 2, 5, 5, 7, 4, 2, 6, 5, 6, 9, 9, 9, 3, 6, 8,
## 7, 6, 8, 5, 9, 9, 6, 7, 5, 6, 7, 7, 6, 7, 6, 7, 3, 7, 7, 9, 5,
## 5, 9, 1, 6, 9, 8, 6, 6, 5, 7, 7, 7, 5, 6, 6, 4, 4, 2, 4, 5, 6,
## 7, 7, 7, 7, 7, 6, 6, 6, 6, 8, 2, 7, 7, 6, 5, 4, 8, 8, 3, 7, 7,
## 7, 5, 6, 5, 6, 4, 5, 6, 6, 8, 4, 8, 5, 6, 9, 8, 5, 4, 6, 7, 6,
## 7, 7, 5, 9, 5, 7, 7, 6, 6, 7, 6, 9, 8, 4, 6, 4, 6, 7, 7, 4, 5,
## 9, 7, 7, 7, 9, 7, 7, 7, 9, 7, 6, 6, 6, 7, 9, 3, 9, 6, 5, 9, 7,
## 9, 9, 3, 6, 7, 5, 8, 3, 9, 3, 7, 5, 4, 5, 4, 7, 7, 7, 2, 6, 7,
## 6, 0, 7, 7, 9, 4, 5, 6, 4, 9, 9, 8, 5, 6, 6, 7, 5, 6, 7, 6, 5,
## 7, 5, 9, 6, 8, 5, 7, 5, 6, 9, 7, 7, 9, 9, 7, 6, 6, 5, 3, 7, 5,
## 0, 9, 6, 9, 7, 7, 7, 3, 4, 7, 7, 5, 4, 6, 7, 3, 6, 6, 3, 8, 8,
## 2, 9, 6, 1, 5, 6, 6, 9, 6, 6, 7, 6, 5, 6, 5, 7, 5, 8, 5, 3, 7,
## 6, 7, 6, 9, 6, 6, 5, 9, 6, 9, 7, 9, 7, 2, 9, 6, 6, 5, 9, 2, 3,
## 7, 9, 4, 7, 7, 9, 8, 7, 0, 7, 7, 7, 6, 9, 6, 7, 7, 5, 9, 5, 5,
## 7, 5, 9, 7, 6, 7, 7, 7, 7, 6, 7, 2, 4, 5, 4, 7, 9, 5, 9, 5, 8,
## 0, 7, 4, 6, 5, 9, 7, 3, 5, 7, 7, 8, 6, 9, 7, 6, 3, 5, 8, 6, 3,
## 6, 4, 9, 6, 3, 7, 7, 2, 5, 7, 5, 9, 9, 4, 7, 7, 7, 7, 5, 7, 6,
## 7, 7, 4, 6, 7, 9, 6, 7, 5, 9), c(0, 2, 2, 2, 1, 6, 2, 2, 0, 0,
## 1, 1, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, 1, 4,
## 1, 1, 2, 1, 1, 2, 1, 0, 3, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 2,
## 2, 0, 0, 1, 3, 2, 2, 1, 1, 1, 0, 2, 2, 0, 1, 0, 0, 0, 0, 1, 1,
## 1, 2, 0, 1, 1, 1, 2, 0, 1, 0, 0, 2, 1, 1, 0, 2, 1, 1, 0, 0, 0,
## 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 1, 1, 1, 0, 2, 1, 1, 6, 2, 0, 0,
## 2, 1, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 0, 2, 2, 2, 2, 1, 0, 4, 2,
## 1, 0, 1, 4, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 1, 1, 1,
## 0, 0, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 3, 0, 1, 0, 1, 0, 1, 0,
## 1, 1, 0, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1,
## 0, 2, 0, 0, 1, 0, 1, 1, 1, 0, 2, 2, 0, 2, 1, 0, 0, 0, 1, 0, 1,
## 0, 4, 0, 1, 1, 1, 0, 2, 1, 1, 1, 0, 0, 0, 2, 0, 3, 1, 2, 1, 1,
## 1, 0, 0, 1, 2, 1, 0, 2, 1, 1, 0, 3, 0, 0, 0, 1, 0, 1, 1, 2, 0,
## 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 2, 4, 2, 1, 0, 1,
## 0, 0, 0, 1, 0, 1, 0, 2, 1, 3, 0, 1, 2, 1, 1, 0, 1, 0, 1, 2, 2,
## 1, 2, 0, 1, 0, 2, 2, 2, 1, 0, 1, 0, 1, 2, 1, 0, 0, 2, 0, 1, 0,
## 1, 1, 1, 0, 2, 0, 4, 1, 2, 3, 0, 0, 2, 1, 1, 2, 1, 0, 1, 1, 0,
## 2, 0, 1, 2, 0, 0, 4, 1, 2, 1, 0, 1, 1, 2, 2, 1, 0, 1, 0, 2, 0,
## 2, 1, 1, 3, 2, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 2, 2, 0, 2, 1, 0,
## 2, 0, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 2, 0, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 0, 0, 0, 1, 1, 0, 1, 2, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2, 2,
## 1, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0,
## 1, 2, 1, 0, 2, 2, 2, 2, 1, 1, 0, 0, 4, 1, 0, 0, 2, 1, 1, 2, 2,
## 0, 0, 1, 0, 0, 5, 0, 1, 0, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 4, 0,
## 2, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 0, 1, 2, 1, 0, 0,
## 1, 1, 1, 0, 2, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 1, 0, 2, 1, 0,
## 1, 0, 2, 2, 2, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 2, 3, 1, 0, 1,
## 0, 2, 2, 1, 2, 3, 4, 0, 1, 2, 1, 1, 1, 1, 1, 0, 2, 0, 0, 1, 1,
## 0, 0, 0, 1, 0, 1, 0, 3, 2, 1, 2, 1, 0, 1, 1, 0, 0, 1, 0, 2, 0,
## 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 1, 0, 1,
## 0, 3, 1, 1, 1, 2, 0, 1, 2, 0, 1, 0, 0, 1, 2, 2, 1, 0, 3, 0, 2,
## 2, 1, 0, 0, 0, 0, 2, 3, 0, 0, 0, 2, 0, 1, 0, 1, 1, 2, 0, 0, 0,
## 1, 1, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2,
## 2, 1, 0, 1, 2, 2, 0, 3, 0, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 3,
## 1, 2, 1, 0, 2, 2, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0,
## 1, 0, 0, 3, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 2, 1,
## 1, 2, 1, 1, 0, 0, 1, 1, 3, 1, 1, 1, 4, 1, 0, 2, 2, 0, 0, 1, 1,
## 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 0, 3, 0, 1, 1, 1,
## 3, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 1,
## 0, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0,
## 0, 2, 0, 1, 0, 0, 0, 2, 1, 0, 1, 1, 1, 2, 5, 0, 1, 0, 0, 1, 0,
## 4, 4, 0, 0, 1, 3, 0, 2, 1, 0, 2, 0, 0, 1, 2, 0, 1, 4, 1, 2, 1,
## 0, 2, 2, 1, 1, 0, 0, 2, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 2, 2,
## 0, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 2, 1, 0, 1, 0, 1, 0, 0,
## 1, 3, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 1, 2, 0,
## 1, 0, 1, 0, 2, 2, 1, 0, 1, 0, 2, 0, 1, 0, 0, 1, 2, 1, 0, 0, 2,
## 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 3, 2, 0, 1, 0, 1, 1, 1, 0,
## 0, 2, 1, 1, 0, 0, 3, 1, 0, 2, 2, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0,
## 1, 1, 0), c(2, 2, 4, 2, 2, 3, 0, 0, 3, 2, 2, 2, 3, 1, 6, 0, 2,
## 2, 2, 0, 0, 2, 2, 0, 1, 3, 0, 0, 4, 4, 3, 2, 1, 4, 1, 3, 0, 1,
## 3, 0, 2, 0, 2, 1, 2, 2, 3, 1, 1, 2, 2, 5, 2, 3, 2, 2, 2, 0, 1,
## 3, 4, 3, 0, 5, 7, 0, 2, 3, 3, 3, 0, 3, 1, 2, 1, 2, 3, 1, 0, 1,
## 4, 2, 1, 3, 4, 3, 0, 0, 6, 2, 1, 0, 3, 6, 0, 0, 0, 1, 2, 5, 0,
## 0, 0, 4, 2, 5, 2, 3, 4, 2, 3, 3, 0, 2, 1, 4, 2, 3, 3, 4, 1, 2,
## 0, 2, 0, 6, 3, 3, 5, 5, 0, 3, 4, 0, 0, 5, 1, 5, 0, 0, 6, 1, 2,
## 2, 2, 1, 3, 0, 0, 2, 2, 2, 2, 3, 1, 3, 1, 2, 4, 1, 3, 1, 3, 3,
## 0, 6, 2, 3, 2, 2, 3, 4, 1, 2, 0, 2, 2, 0, 2, 1, 0, 4, 0, 0, 1,
## 8, 3, 2, 2, 2, 0, 0, 0, 4, 2, 3, 2, 2, 2, 0, 1, 4, 0, 4, 0, 1,
## 3, 4, 3, 3, 6, 2, 0, 3, 2, 3, 4, 1, 1, 2, 1, 5, 3, 5, 2, 3, 2,
## 4, 3, 3, 3, 0, 1, 4, 2, 3, 0, 3, 3, 3, 2, 2, 0, 1, 2, 0, 2, 2,
## 0, 2, 2, 0, 4, 2, 3, 0, 7, 3, 3, 2, 2, 0, 3, 2, 5, 1, 3, 4, 2,
## 0, 2, 1, 2, 2, 4, 4, 5, 5, 5, 3, 3, 0, 4, 5, 0, 2, 1, 4, 2, 2,
## 0, 2, 3, 3, 2, 5, 3, 2, 6, 1, 0, 2, 2, 1, 2, 4, 4, 2, 3, 3, 2,
## 6, 2, 3, 3, 2, 2, 0, 4, 0, 4, 2, 3, 1, 0, 2, 2, 4, 1, 6, 0, 2,
## 3, 0, 6, 0, 3, 2, 1, 2, 0, 4, 2, 2, 1, 4, 0, 0, 2, 0, 2, 0, 0,
## 6, 5, 1, 0, 2, 2, 3, 0, 3, 0, 4, 0, 3, 0, 2, 1, 2, 2, 4, 2, 3,
## 1, 0, 3, 2, 4, 6, 2, 2, 0, 0, 3, 5, 2, 2, 3, 1, 2, 2, 2, 2, 1,
## 0, 3, 2, 5, 0, 4, 0, 2, 3, 3, 2, 0, 2, 2, 4, 3, 5, 0, 0, 3, 2,
## 5, 3, 6, 3, 6, 1, 2, 4, 0, 3, 2, 0, 6, 3, 4, 2, 2, 3, 0, 2, 5,
## 3, 4, 0, 2, 4, 2, 4, 2, 2, 2, 0, 4, 3, 4, 2, 7, 2, 0, 4, 5, 2,
## 2, 2, 3, 2, 1, 2, 2, 3, 3, 5, 2, 2, 4, 4, 1, 0, 1, 3, 0, 4, 2,
## 7, 3, 4, 0, 2, 3, 0, 6, 4, 2, 6, 3, 2, 2, 0, 3, 2, 2, 2, 4, 2,
## 1, 0, 2, 2, 2, 3, 0, 3, 0, 2, 0, 4, 0, 2, 2, 3, 0, 8, 5, 0, 2,
## 7, 2, 1, 2, 2, 0, 0, 0, 2, 2, 1, 5, 2, 4, 2, 0, 0, 0, 0, 0, 0,
## 2, 2, 6, 0, 2, 3, 4, 2, 2, 4, 6, 2, 2, 4, 0, 5, 2, 4, 0, 5, 2,
## 2, 4, 0, 3, 4, 0, 3, 2, 3, 3, 9, 1, 0, 1, 2, 0, 6, 4, 0, 2, 4,
## 5, 0, 4, 3, 2, 6, 2, 2, 3, 2, 2, 5, 0, 0, 0, 3, 0, 0, 4, 1, 5,
## 1, 0, 5, 0, 0, 2, 3, 0, 0, 3, 3, 4, 2, 2, 2, 2, 2, 4, 1, 5, 1,
## 2, 2, 4, 2, 0, 2, 2, 0, 0, 8, 0, 0, 3, 6, 2, 3, 2, 5, 7, 3, 3,
## 0, 0, 0, 0, 5, 3, 1, 2, 3, 1, 3, 0, 0, 3, 2, 3, 3, 2, 2, 2, 2,
## 3, 2, 4, 2, 2, 0, 4, 4, 0, 8, 3, 0, 0, 2, 1, 4, 2, 2, 0, 2, 3,
## 0, 5, 5, 5, 4, 3, 3, 2, 2, 2, 0, 2, 3, 0, 3, 3, 1, 7, 0, 0, 3,
## 3, 5, 0, 1, 6, 2, 2, 2, 4, 3, 3, 2, 4, 4, 2, 3, 1, 2, 1, 4, 3,
## 0, 1, 4, 5, 3, 0, 3, 2, 2, 4, 0, 3, 1, 2, 2, 2, 2, 3, 0, 1, 5,
## 2, 3, 3, 2, 2, 2, 4, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 3, 3, 3, 1,
## 0, 5, 0, 3, 4, 0, 2, 0, 0, 4, 3, 1, 3, 1, 4, 0, 4, 2, 3, 4, 3,
## 5, 2, 2, 2, 6, 3, 0, 3, 9, 2, 2, 0, 5, 4, 3, 4, 0, 0, 1, 3, 3,
## 3, 2, 4, 3, 2, 3, 4, 2, 3, 0, 3, 1, 4, 2, 4, 3, 0, 2, 2, 0, 0,
## 0, 2, 3, 4, 5, 2, 3, 4, 0, 2, 0, 2, 2, 2, 3, 2, 2, 2, 4, 2, 3,
## 0, 5, 3, 2, 6, 1, 1, 5, 0, 3, 5, 4, 3, 2, 0, 3, 2, 2, 2, 4, 3,
## 3, 2, 3, 1, 3, 6, 2, 3, 2, 2, 0, 2, 1, 3, 0, 2, 0, 0, 0, 2, 5,
## 0, 3, 2, 3, 0, 5, 4, 2, 0, 5, 2, 2, 0, 1, 2, 6, 2, 2, 2, 3, 0,
## 3, 2, 2, 3, 0, 4, 4, 2, 4, 0, 0, 3, 0, 2, 2, 2, 3, 2, 5, 4, 3,
## 5, 2, 0, 3, 0, 4, 1, 9, 2, 4, 2, 4, 0, 0, 6, 3, 2, 2, 1, 3, 0,
## 0, 3, 6, 4, 1, 0, 4, 3, 4, 0, 3, 5, 2, 2, 7, 3, 2, 4, 0, 0, 3,
## 1, 2, 0, 0, 4, 2, 3, 2, 2, 5, 3, 2, 0, 3, 2, 3, 0), c(1, 0, 4,
## 2, 2, 3, 0, 0, 3, 2, 0, 2, 3, 1, 5, 0, 0, 0, 1, 0, 0, 0, 1, 0,
## 1, 2, 0, 0, 0, 4, 3, 6, 1, 4, 1, 1, 0, 1, 0, 0, 0, 2, 2, 1, 1,
## 3, 4, 1, 1, 2, 0, 5, 2, 4, 1, 0, 6, 1, 1, 1, 5, 2, 0, 5, 7, 0,
## 1, 2, 3, 3, 0, 4, 2, 2, 2, 2, 2, 1, 0, 1, 3, 0, 1, 2, 2, 3, 0,
## 0, 5, 3, 0, 0, 1, 6, 2, 0, 2, 5, 2, 4, 0, 0, 0, 4, 0, 3, 2, 4,
## 4, 0, 0, 3, 0, 1, 1, 5, 2, 3, 0, 2, 1, 0, 0, 1, 0, 6, 3, 3, 5,
## 5, 0, 2, 3, 0, 0, 4, 1, 3, 0, 0, 6, 1, 0, 2, 1, 0, 2, 0, 0, 2,
## 0, 2, 1, 0, 1, 1, 1, 1, 4, 1, 2, 1, 3, 0, 0, 3, 2, 3, 0, 1, 2,
## 4, 0, 1, 0, 0, 2, 0, 0, 1, 0, 3, 0, 0, 1, 7, 2, 1, 2, 2, 3, 0,
## 0, 3, 0, 0, 2, 0, 2, 0, 1, 4, 0, 1, 0, 0, 2, 3, 3, 2, 3, 0, 0,
## 0, 0, 2, 4, 1, 1, 1, 1, 5, 2, 3, 3, 1, 2, 4, 2, 3, 3, 0, 1, 0,
## 2, 2, 0, 3, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 2, 1, 3,
## 0, 6, 3, 3, 2, 2, 0, 8, 2, 5, 1, 2, 4, 2, 0, 0, 1, 5, 3, 0, 4,
## 4, 5, 5, 3, 0, 2, 4, 6, 0, 4, 1, 7, 1, 2, 0, 3, 0, 2, 2, 5, 0,
## 0, 5, 0, 0, 2, 2, 0, 2, 3, 2, 0, 5, 2, 2, 6, 1, 2, 2, 1, 0, 0,
## 3, 0, 4, 0, 2, 1, 0, 2, 0, 2, 2, 3, 0, 1, 0, 0, 6, 0, 2, 2, 1,
## 2, 0, 3, 2, 2, 1, 4, 0, 2, 0, 3, 2, 0, 0, 3, 5, 1, 0, 4, 1, 3,
## 0, 3, 0, 3, 0, 9, 0, 2, 0, 2, 0, 4, 2, 1, 1, 0, 1, 0, 4, 5, 0,
## 0, 0, 0, 2, 1, 2, 1, 3, 0, 4, 2, 9, 2, 0, 0, 2, 1, 4, 0, 3, 0,
## 2, 2, 3, 2, 2, 1, 0, 3, 2, 1, 0, 0, 3, 0, 0, 0, 4, 2, 6, 2, 0,
## 4, 0, 4, 1, 0, 5, 2, 4, 1, 2, 0, 0, 0, 5, 3, 3, 0, 0, 4, 0, 4,
## 1, 0, 2, 0, 0, 2, 3, 2, 6, 2, 1, 4, 5, 2, 2, 2, 6, 2, 1, 1, 2,
## 3, 2, 5, 0, 0, 3, 4, 1, 3, 1, 5, 0, 2, 2, 7, 3, 4, 0, 1, 4, 0,
## 3, 3, 8, 4, 2, 2, 2, 0, 2, 1, 0, 4, 3, 2, 1, 2, 2, 2, 0, 4, 0,
## 3, 0, 2, 0, 3, 0, 0, 2, 3, 0, 8, 5, 4, 0, 4, 2, 1, 2, 1, 0, 0,
## 0, 3, 2, 3, 5, 3, 3, 1, 0, 0, 0, 0, 0, 0, 3, 1, 6, 0, 1, 3, 4,
## 2, 2, 0, 6, 1, 1, 4, 0, 5, 1, 3, 0, 5, 1, 2, 4, 0, 0, 4, 0, 0,
## 2, 3, 3, 9, 1, 2, 1, 0, 3, 6, 3, 0, 2, 7, 8, 0, 3, 4, 0, 5, 2,
## 2, 3, 0, 0, 5, 0, 0, 0, 2, 0, 0, 3, 0, 3, 1, 0, 3, 1, 0, 0, 2,
## 0, 0, 2, 3, 3, 0, 0, 2, 1, 2, 3, 1, 5, 0, 1, 3, 0, 0, 0, 2, 3,
## 0, 0, 7, 0, 0, 2, 4, 2, 0, 0, 3, 4, 2, 2, 0, 3, 3, 0, 5, 2, 2,
## 1, 3, 1, 2, 0, 0, 4, 0, 3, 3, 0, 2, 2, 0, 2, 3, 4, 2, 2, 0, 3,
## 3, 0, 8, 3, 4, 0, 0, 1, 2, 1, 2, 1, 4, 3, 0, 3, 4, 5, 4, 2, 2,
## 1, 2, 2, 0, 2, 3, 0, 3, 3, 1, 6, 0, 0, 3, 2, 3, 0, 1, 3, 2, 2,
## 1, 4, 2, 2, 1, 3, 1, 0, 3, 0, 2, 1, 3, 3, 1, 1, 4, 4, 3, 0, 2,
## 0, 0, 4, 0, 2, 4, 3, 1, 0, 2, 5, 0, 1, 5, 1, 1, 0, 2, 6, 2, 3,
## 0, 0, 0, 0, 0, 3, 0, 3, 0, 1, 2, 3, 2, 1, 0, 4, 0, 3, 4, 0, 2,
## 0, 0, 4, 3, 1, 2, 1, 4, 1, 4, 1, 3, 4, 4, 3, 5, 0, 0, 6, 5, 0,
## 2, 7, 4, 0, 0, 5, 2, 0, 0, 5, 1, 1, 3, 3, 2, 4, 3, 2, 2, 1, 4,
## 0, 4, 0, 3, 1, 3, 2, 1, 3, 0, 2, 2, 0, 2, 0, 0, 2, 4, 7, 1, 0,
## 2, 0, 1, 0, 0, 1, 1, 4, 2, 0, 0, 4, 6, 2, 0, 4, 1, 0, 6, 1, 1,
## 5, 0, 1, 5, 2, 3, 3, 0, 3, 2, 4, 2, 4, 0, 0, 0, 0, 1, 2, 4, 0,
## 2, 2, 2, 0, 2, 0, 2, 1, 2, 0, 0, 0, 3, 5, 1, 0, 2, 0, 0, 6, 4,
## 0, 0, 5, 1, 1, 3, 1, 3, 6, 2, 1, 0, 0, 1, 3, 3, 0, 0, 0, 4, 2,
## 2, 3, 0, 0, 3, 0, 1, 4, 0, 1, 0, 5, 4, 3, 5, 1, 3, 2, 0, 0, 2,
## 7, 2, 4, 1, 1, 0, 0, 3, 3, 0, 0, 0, 3, 0, 0, 3, 6, 3, 1, 0, 3,
## 3, 3, 0, 1, 7, 3, 2, 6, 9, 1, 4, 3, 2, 3, 0, 2, 0, 0, 3, 2, 0,
## 0, 0, 1, 3, 2, 0, 5, 1, 2, 0), c(2, 4, 4, 3, 4, 5, 3, 5, 3, 2,
## 3, 3, 4, 4, 3, 5, 6, 2, 3, 6, 3, 2, 3, 4, 3, 3, 3, 4, 0, 1, 3,
## 0, 2, 4, 3, 4, 6, 5, 0, 3, 0, 3, 3, 7, 3, 2, 3, 1, 5, 1, 6, 3,
## 4, 2, 3, 0, 3, 2, 7, 4, 4, 4, 5, 4, 2, 2, 4, 4, 4, 4, 4, 5, 5,
## 3, 3, 4, 4, 8, 7, 4, 3, 9, 4, 3, 5, 2, 5, 3, 3, 4, 4, 0, 4, 2,
## 5, 4, 4, 1, 4, 3, 2, 4, 2, 2, 3, 0, 4, 2, 4, 0, 2, 5, 5, 3, 4,
## 4, 3, 3, 6, 3, 6, 0, 4, 3, 3, 2, 5, 4, 3, 3, 2, 6, 2, 4, 4, 2,
## 4, 2, 5, 6, 3, 3, 3, 0, 1, 1, 0, 3, 1, 3, 3, 6, 2, 2, 2, 6, 1,
## 4, 4, 5, 4, 5, 1, 3, 3, 2, 4, 5, 4, 2, 3, 2, 6, 3, 4, 3, 2, 4,
## 1, 3, 3, 2, 3, 5, 4, 1, 0, 4, 4, 3, 4, 1, 6, 3, 4, 5, 4, 3, 3,
## 6, 4, 2, 5, 1, 0, 5, 4, 4, 1, 4, 5, 4, 5, 2, 6, 2, 3, 1, 4, 4,
## 6, 4, 3, 3, 4, 6, 3, 2, 4, 5, 4, 4, 1, 0, 2, 4, 4, 2, 2, 2, 3,
## 4, 4, 5, 0, 6, 2, 4, 5, 2, 2, 4, 6, 1, 4, 3, 2, 3, 5, 3, 5, 5,
## 1, 5, 3, 2, 3, 4, 3, 1, 5, 0, 3, 5, 5, 3, 3, 4, 4, 4, 5, 5, 4,
## 3, 4, 1, 4, 2, 4, 2, 4, 5, 4, 5, 4, 3, 5, 2, 4, 5, 3, 3, 3, 5,
## 3, 2, 3, 0, 3, 0, 6, 2, 2, 4, 5, 3, 1, 4, 3, 3, 3, 3, 3, 3, 9,
## 3, 3, 5, 2, 5, 3, 6, 4, 2, 2, 2, 0, 4, 5, 3, 4, 2, 2, 3, 3, 3,
## 4, 5, 0, 3, 4, 4, 2, 2, 3, 4, 0, 4, 5, 5, 4, 4, 4, 3, 5, 0, 5,
## 2, 5, 3, 4, 2, 4, 5, 2, 0, 0, 5, 4, 2, 0, 1, 4, 5, 1, 7, 3, 3,
## 3, 0, 0, 0, 0, 3, 4, 2, 3, 4, 2, 3, 2, 6, 4, 1, 3, 3, 3, 5, 6,
## 4, 3, 2, 0, 4, 4, 2, 0, 3, 4, 1, 3, 7, 2, 4, 2, 3, 4, 0, 3, 4,
## 1, 4, 5, 5, 2, 5, 2, 3, 4, 3, 3, 2, 2, 2, 4, 3, 4, 6, 5, 2, 0,
## 3, 3, 3, 6, 3, 3, 2, 4, 6, 0, 2, 1, 6, 5, 3, 2, 3, 2, 1, 2, 4,
## 1, 2, 4, 3, 4, 5, 6, 2, 3, 4, 0, 4, 4, 1, 2, 2, 1, 2, 2, 3, 6,
## 4, 2, 3, 2, 4, 2, 3, 2, 2, 3, 2, 3, 4, 4, 4, 5, 3, 2, 4, 2, 5,
## 3, 2, 2, 1, 3, 2, 1, 3, 3, 4, 5, 1, 3, 6, 3, 2, 4, 3, 3, 2, 4,
## 2, 6, 4, 7, 6, 6, 2, 5, 4, 3, 4, 1, 0, 3, 4, 4, 4, 3, 4, 0, 1,
## 4, 3, 7, 3, 5, 0, 7, 5, 4, 6, 5, 1, 2, 4, 3, 3, 2, 0, 1, 4, 6,
## 5, 4, 2, 4, 5, 3, 2, 0, 6, 3, 4, 3, 3, 3, 4, 3, 5, 4, 0, 4, 3,
## 3, 3, 3, 1, 0, 5, 0, 4, 4, 2, 3, 3, 3, 1, 0, 5, 2, 1, 2, 4, 0,
## 3, 6, 3, 4, 3, 2, 3, 4, 2, 0, 0, 5, 3, 3, 5, 6, 2, 1, 4, 4, 4,
## 3, 2, 2, 4, 3, 4, 5, 5, 3, 2, 6, 4, 2, 5, 1, 5, 3, 2, 6, 4, 3,
## 2, 3, 5, 4, 6, 3, 0, 0, 4, 3, 5, 1, 1, 3, 4, 3, 1, 1, 2, 5, 7,
## 4, 4, 2, 4, 1, 3, 2, 5, 3, 4, 3, 4, 2, 4, 6, 5, 3, 6, 5, 4, 4,
## 1, 4, 3, 0, 5, 6, 4, 2, 4, 1, 1, 4, 4, 3, 3, 1, 5, 2, 7, 4, 4,
## 0, 2, 1, 6, 2, 4, 2, 6, 2, 4, 2, 3, 4, 0, 2, 0, 3, 3, 4, 4, 3,
## 3, 4, 4, 4, 2, 0, 3, 2, 5, 5, 1, 0, 3, 4, 5, 4, 5, 5, 3, 4, 2,
## 2, 4, 2, 3, 4, 3, 3, 2, 0, 3, 3, 2, 2, 4, 6, 5, 3, 4, 4, 4, 3,
## 3, 7, 4, 4, 2, 3, 3, 4, 4, 3, 1, 2, 3, 6, 0, 0, 0, 3, 0, 1, 5,
## 1, 3, 2, 6, 3, 4, 1, 4, 4, 4, 2, 2, 5, 1, 2, 2, 6, 2, 3, 3, 2,
## 1, 4, 3, 4, 4, 0, 2, 4, 5, 3, 2, 2, 3, 2, 5, 4, 2, 4, 3, 4, 1,
## 4, 3, 2, 4, 4, 3, 4, 4, 0, 2, 4, 1, 2, 1, 4, 9, 4, 4, 6, 4, 5,
## 3, 4, 5, 4, 3, 4, 1, 6, 7, 4, 1, 3, 2, 7, 3, 6, 3, 5, 3, 3, 4,
## 3, 3, 3, 6, 1, 2, 4, 6, 3, 3, 5, 5, 3, 4, 0, 3, 2, 3, 2, 3, 1,
## 2, 3, 6, 3, 5, 3, 6, 3, 4, 0, 5, 0, 2, 3, 6, 4, 4, 5, 4, 4, 0,
## 4, 3, 5, 3, 3, 4, 4, 0, 2, 4, 4, 1, 4, 5, 0, 3, 2, 4, 1, 3, 4,
## 4, 2, 6, 3, 4, 4, 3, 4, 4, 2, 2, 4, 5, 2, 3, 4, 4, 4, 0, 3, 5,
## 0, 0, 2, 1, 4, 5, 2, 4, 5, 6, 4, 4, 4, 1, 4, 3, 2, 4, 5, 6, 3,
## 2, 5, 5), c(6, 5, 2, 4, 4, 2, 6, 4, 3, 6, 6, 5, 3, 5, 1, 4, 3,
## 7, 6, 3, 6, 7, 6, 5, 6, 5, 6, 5, 9, 5, 3, 3, 7, 3, 6, 5, 3, 3,
## 9, 6, 9, 4, 5, 2, 5, 5, 3, 8, 4, 6, 3, 3, 3, 4, 6, 9, 1, 6, 2,
## 5, 1, 4, 4, 0, 1, 7, 4, 4, 3, 2, 5, 1, 3, 5, 5, 4, 3, 1, 2, 5,
## 4, 0, 5, 5, 3, 4, 4, 6, 2, 3, 5, 8, 4, 1, 2, 5, 3, 4, 3, 2, 7,
## 5, 7, 3, 6, 6, 4, 4, 2, 9, 7, 2, 4, 5, 4, 2, 4, 4, 3, 4, 3, 9,
## 5, 5, 6, 2, 1, 3, 3, 2, 7, 1, 4, 5, 5, 3, 4, 5, 4, 3, 1, 5, 6,
## 7, 8, 8, 7, 6, 8, 5, 6, 2, 7, 7, 7, 2, 8, 5, 2, 4, 3, 4, 6, 6,
## 6, 4, 3, 2, 5, 7, 4, 3, 3, 6, 5, 6, 5, 5, 8, 5, 6, 5, 6, 4, 4,
## 1, 7, 4, 4, 5, 3, 8, 3, 4, 5, 4, 3, 6, 4, 3, 4, 3, 4, 8, 8, 4,
## 3, 2, 6, 4, 1, 5, 4, 7, 4, 5, 3, 8, 5, 4, 3, 1, 5, 4, 3, 2, 5,
## 3, 3, 1, 3, 5, 7, 9, 5, 4, 5, 5, 6, 7, 4, 4, 5, 3, 9, 3, 7, 5,
## 4, 7, 5, 5, 1, 8, 3, 6, 1, 3, 2, 4, 2, 4, 0, 3, 2, 7, 4, 2, 4,
## 8, 4, 8, 1, 1, 4, 3, 2, 2, 1, 3, 4, 3, 1, 1, 5, 5, 4, 1, 5, 6,
## 5, 2, 5, 3, 4, 2, 4, 7, 1, 4, 6, 4, 5, 4, 5, 5, 4, 9, 2, 7, 2,
## 1, 6, 4, 3, 6, 8, 5, 4, 6, 3, 6, 5, 6, 0, 4, 6, 2, 5, 1, 6, 3,
## 5, 7, 2, 7, 7, 4, 3, 4, 5, 4, 6, 5, 6, 3, 5, 4, 9, 4, 4, 5, 7,
## 4, 1, 5, 9, 2, 4, 3, 5, 3, 5, 4, 4, 0, 4, 5, 4, 4, 5, 3, 4, 3,
## 6, 9, 8, 4, 2, 2, 9, 8, 5, 4, 6, 1, 4, 6, 3, 9, 5, 7, 0, 4, 5,
## 7, 5, 4, 3, 6, 5, 3, 4, 6, 4, 4, 4, 3, 3, 3, 4, 6, 9, 5, 3, 7,
## 9, 6, 2, 6, 0, 1, 7, 3, 7, 3, 5, 9, 2, 4, 5, 4, 3, 4, 7, 4, 3,
## 4, 2, 6, 6, 4, 7, 4, 4, 6, 3, 3, 4, 6, 6, 4, 0, 5, 3, 3, 1, 5,
## 3, 2, 3, 5, 7, 3, 3, 4, 5, 1, 7, 8, 5, 2, 8, 4, 4, 2, 5, 3, 1,
## 0, 3, 3, 9, 4, 2, 8, 4, 5, 1, 4, 5, 5, 1, 5, 5, 6, 7, 2, 5, 5,
## 6, 5, 4, 6, 6, 2, 5, 3, 4, 5, 7, 3, 7, 4, 4, 4, 7, 1, 1, 4, 8,
## 3, 5, 5, 3, 8, 6, 3, 6, 5, 4, 3, 1, 5, 3, 7, 3, 5, 2, 3, 3, 7,
## 2, 4, 0, 5, 8, 6, 3, 4, 3, 5, 0, 4, 8, 5, 5, 1, 2, 4, 4, 4, 1,
## 3, 2, 3, 4, 5, 7, 5, 4, 4, 5, 0, 8, 4, 3, 4, 3, 1, 3, 4, 4, 1,
## 1, 3, 4, 2, 6, 2, 5, 4, 4, 4, 5, 4, 5, 6, 6, 4, 6, 8, 6, 4, 6,
## 5, 5, 5, 5, 6, 6, 6, 9, 4, 6, 6, 4, 5, 9, 5, 2, 4, 3, 5, 3, 6,
## 4, 5, 9, 9, 4, 5, 3, 4, 3, 0, 8, 5, 4, 2, 4, 7, 7, 3, 2, 4, 4,
## 4, 4, 4, 3, 2, 5, 3, 8, 1, 6, 6, 3, 5, 3, 7, 4, 2, 5, 1, 4, 9,
## 7, 3, 2, 2, 6, 8, 4, 2, 6, 1, 6, 4, 4, 2, 4, 4, 6, 4, 8, 3, 5,
## 4, 3, 2, 1, 1, 6, 4, 3, 3, 5, 3, 3, 3, 5, 6, 3, 6, 3, 4, 3, 3,
## 5, 3, 8, 7, 3, 4, 5, 6, 5, 3, 5, 2, 3, 4, 9, 5, 8, 1, 6, 3, 4,
## 3, 6, 2, 3, 3, 5, 7, 7, 9, 2, 6, 4, 1, 4, 5, 5, 4, 1, 7, 8, 2,
## 7, 3, 4, 6, 3, 4, 3, 4, 5, 4, 4, 6, 3, 7, 5, 5, 7, 5, 3, 4, 5,
## 7, 5, 6, 3, 3, 7, 3, 3, 4, 2, 3, 4, 3, 6, 2, 2, 2, 4, 4, 2, 3,
## 3, 0, 6, 8, 2, 2, 3, 7, 2, 5, 6, 8, 4, 2, 8, 6, 3, 3, 6, 3, 6,
## 4, 2, 3, 5, 6, 4, 5, 7, 3, 3, 5, 6, 4, 6, 8, 3, 6, 4, 3, 9, 5,
## 5, 4, 5, 4, 0, 6, 7, 3, 5, 6, 5, 6, 5, 8, 2, 4, 7, 5, 2, 1, 4,
## 5, 5, 7, 5, 3, 6, 8, 0, 0, 5, 1, 2, 3, 2, 6, 3, 3, 2, 4, 2, 8,
## 3, 2, 5, 8, 4, 4, 2, 5, 1, 4, 4, 4, 6, 3, 5, 4, 6, 3, 8, 5, 0,
## 3, 6, 5, 4, 4, 1, 1, 9, 6, 3, 6, 6, 4, 7, 5, 0, 2, 5, 4, 6, 3,
## 3, 3, 9, 4, 9, 4, 4, 2, 2, 5, 4, 3, 5, 8, 2, 6, 4, 6, 1, 3, 2,
## 4, 6, 3, 4, 8, 5, 3, 2, 4, 3, 5, 8, 6, 5, 3, 5, 3, 6, 5, 2, 6,
## 5, 2, 2, 5, 5, 4, 5, 3, 2, 5, 5, 2, 4, 3, 3, 0, 6, 5, 2, 4, 5,
## 5, 2, 3, 5, 3, 4, 8, 5, 6, 6, 3, 3, 3, 2, 6, 3, 4), c(1, 0, 0,
## 3, 5, 0, 0, 0, 0, 0, 4, 1, 1, 2, 2, 0, 2, 2, 5, 0, 0, 0, 3, 0,
## 1, 1, 3, 2, 0, 0, 2, 1, 2, 1, 1, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0,
## 1, 1, 1, 1, 0, 0, 2, 1, 3, 1, 0, 4, 2, 0, 1, 2, 1, 3, 0, 0, 2,
## 1, 4, 0, 0, 2, 1, 2, 3, 3, 0, 0, 5, 4, 2, 1, 0, 5, 1, 1, 2, 4,
## 2, 2, 1, 0, 5, 3, 1, 2, 0, 0, 5, 1, 1, 1, 3, 2, 2, 4, 0, 5, 3,
## 0, 0, 4, 0, 0, 4, 0, 3, 3, 0, 6, 0, 0, 0, 0, 0, 5, 1, 1, 7, 2,
## 2, 4, 1, 1, 2, 3, 1, 1, 1, 4, 6, 1, 4, 1, 1, 0, 0, 0, 5, 0, 3,
## 3, 3, 0, 1, 3, 2, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 1, 2, 0, 1, 1,
## 2, 2, 1, 0, 1, 4, 3, 1, 1, 3, 0, 0, 0, 1, 1, 0, 2, 2, 3, 3, 0,
## 0, 2, 0, 0, 0, 0, 3, 0, 2, 0, 3, 4, 2, 0, 0, 0, 0, 2, 2, 0, 2,
## 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 1, 2, 5, 1, 1, 1, 3, 2, 1, 0,
## 0, 4, 0, 0, 0, 4, 3, 4, 0, 1, 0, 5, 8, 0, 0, 2, 1, 2, 6, 3, 0,
## 0, 1, 0, 2, 1, 2, 3, 8, 0, 1, 0, 1, 0, 3, 1, 0, 3, 2, 0, 0, 0,
## 2, 0, 1, 1, 0, 0, 1, 3, 2, 3, 1, 2, 4, 0, 0, 0, 0, 3, 5, 2, 0,
## 5, 0, 0, 0, 3, 1, 2, 2, 3, 0, 0, 3, 1, 0, 7, 1, 4, 2, 5, 1, 1,
## 2, 2, 0, 3, 1, 4, 0, 2, 4, 1, 2, 2, 1, 1, 0, 1, 7, 0, 0, 1, 0,
## 3, 4, 0, 0, 0, 0, 0, 0, 4, 0, 3, 2, 0, 3, 0, 1, 1, 0, 0, 1, 0,
## 0, 3, 2, 2, 3, 0, 0, 2, 0, 2, 2, 1, 5, 1, 3, 0, 1, 2, 0, 1, 0,
## 1, 0, 0, 3, 8, 3, 1, 2, 2, 4, 1, 0, 1, 4, 4, 1, 2, 1, 0, 0, 1,
## 5, 3, 2, 1, 0, 6, 0, 2, 2, 1, 4, 8, 2, 2, 5, 3, 1, 1, 0, 2, 4,
## 1, 2, 1, 1, 0, 2, 3, 0, 0, 0, 0, 0, 0, 2, 2, 2, 6, 7, 1, 8, 0,
## 2, 0, 0, 2, 0, 0, 0, 3, 3, 2, 4, 1, 1, 0, 1, 3, 4, 4, 2, 1, 1,
## 0, 0, 1, 3, 1, 0, 0, 1, 1, 1, 3, 2, 0, 2, 0, 0, 1, 2, 0, 3, 1,
## 0, 0, 0, 0, 0, 2, 2, 4, 1, 2, 3, 0, 2, 2, 1, 0, 2, 0, 2, 0, 2,
## 0, 0, 2, 4, 2, 0, 2, 3, 2, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 6, 3,
## 1, 1, 1, 1, 1, 1, 2, 0, 7, 0, 5, 2, 0, 1, 0, 1, 2, 2, 0, 0, 9,
## 5, 2, 0, 3, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0,
## 3, 0, 1, 2, 6, 2, 4, 0, 3, 1, 2, 0, 1, 2, 8, 2, 2, 0, 0, 2, 1,
## 5, 0, 0, 8, 5, 0, 4, 0, 2, 5, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 3,
## 0, 3, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 2, 0, 2, 1, 0, 0, 3, 0, 2,
## 0, 1, 0, 0, 5, 4, 1, 1, 0, 2, 0, 0, 4, 2, 1, 7, 0, 0, 0, 1, 2,
## 0, 2, 0, 0, 7, 0, 1, 5, 2, 2, 0, 3, 3, 3, 0, 1, 1, 4, 0, 4, 1,
## 0, 1, 0, 4, 2, 4, 0, 0, 1, 4, 2, 2, 1, 2, 0, 0, 4, 1, 2, 0, 4,
## 2, 0, 2, 2, 0, 1, 5, 4, 1, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 5, 0,
## 3, 0, 2, 0, 1, 2, 0, 0, 0, 0, 1, 4, 0, 2, 0, 1, 2, 1, 0, 0, 0,
## 4, 0, 2, 5, 0, 0, 0, 0, 0, 5, 1, 2, 3, 3, 0, 2, 0, 1, 1, 2, 1,
## 0, 0, 0, 2, 2, 0, 2, 1, 6, 1, 1, 1, 1, 4, 1, 0, 0, 1, 2, 3, 1,
## 0, 0, 2, 0, 4, 1, 4, 2, 3, 0, 0, 2, 2, 4, 0, 0, 0, 0, 5, 3, 2,
## 0, 0, 4, 3, 2, 0, 1, 0, 3, 5, 4, 2, 0, 4, 4, 0, 2, 0, 3, 0, 0,
## 2, 2, 0, 3, 0, 1, 0, 2, 1, 0, 2, 0, 0, 0, 0, 4, 1, 1, 1, 2, 1,
## 0, 3, 1, 6, 0, 0, 0, 2, 2, 1, 0, 1, 4, 4, 0, 0, 3, 0, 2, 2, 1,
## 0, 0, 2, 1, 2, 1, 0, 1, 1, 1, 0, 3, 2, 0, 6, 4, 0, 1, 2, 0, 0,
## 1, 2, 1, 0, 1, 0, 1, 4, 3, 0, 2, 5, 1, 0, 4, 0, 1, 0, 3, 1, 1,
## 0, 0, 3, 3, 1, 7, 1, 1, 3, 3, 0, 0, 0, 4, 0, 2, 0, 0, 0, 1, 0,
## 3, 0, 8, 0, 2, 0, 1, 0, 0, 0, 1, 1, 1, 3, 5, 1, 3, 2, 0, 0, 1,
## 0, 1, 1, 1, 2, 0, 0, 0, 1, 0, 7, 4, 2, 2, 1, 1, 0, 0, 0, 1, 3,
## 1, 2, 4, 2, 4, 0, 0, 0, 0, 3, 0, 0, 4, 0, 1, 4, 2, 0, 1, 1, 0,
## 0, 0, 1, 0, 0, 0, 3, 1, 2, 0), c(2, 5, 5, 4, 4, 5, 4, 3, 1, 4,
## 3, 7, 4, 4, 6, 3, 6, 1, 4, 0, 0, 2, 5, 2, 7, 2, 5, 0, 0, 2, 5,
## 8, 2, 3, 7, 5, 7, 3, 3, 1, 0, 5, 4, 2, 4, 3, 3, 4, 4, 2, 2, 3,
## 2, 3, 2, 4, 5, 4, 3, 3, 4, 3, 4, 7, 7, 3, 2, 3, 7, 1, 5, 5, 3,
## 4, 6, 4, 3, 4, 3, 5, 3, 0, 4, 2, 4, 3, 1, 4, 5, 1, 6, 4, 2, 1,
## 5, 4, 0, 4, 5, 4, 1, 6, 3, 3, 2, 0, 4, 5, 5, 0, 4, 5, 3, 5, 4,
## 2, 1, 4, 3, 3, 2, 0, 2, 3, 2, 1, 5, 2, 3, 6, 4, 3, 2, 4, 6, 4,
## 2, 3, 1, 2, 6, 4, 6, 8, 1, 1, 3, 3, 6, 4, 5, 5, 3, 7, 5, 2, 5,
## 2, 2, 4, 3, 1, 1, 6, 4, 1, 2, 4, 4, 3, 4, 3, 0, 2, 4, 1, 3, 6,
## 1, 4, 4, 5, 4, 9, 2, 4, 6, 3, 4, 5, 4, 4, 0, 2, 0, 5, 7, 3, 1,
## 5, 2, 3, 5, 4, 4, 8, 6, 4, 1, 5, 6, 0, 4, 2, 4, 5, 3, 5, 5, 3,
## 3, 6, 2, 5, 4, 2, 2, 3, 3, 5, 3, 4, 5, 0, 2, 3, 0, 2, 4, 4, 4,
## 3, 0, 5, 4, 3, 1, 0, 3, 0, 3, 6, 1, 2, 3, 3, 7, 1, 4, 3, 4, 5,
## 1, 0, 4, 2, 3, 0, 4, 2, 0, 4, 4, 5, 4, 3, 2, 8, 6, 4, 2, 4, 7,
## 2, 3, 2, 6, 4, 1, 3, 2, 5, 4, 4, 4, 6, 2, 3, 2, 8, 0, 4, 3, 3,
## 4, 4, 3, 0, 4, 3, 3, 1, 4, 3, 3, 4, 1, 6, 2, 5, 3, 5, 2, 4, 0,
## 3, 3, 4, 4, 6, 2, 6, 3, 5, 2, 5, 6, 3, 3, 4, 4, 1, 2, 4, 3, 3,
## 2, 3, 0, 3, 4, 4, 4, 1, 4, 6, 5, 3, 1, 3, 2, 3, 3, 2, 4, 3, 4,
## 6, 8, 3, 7, 3, 4, 5, 4, 5, 3, 4, 0, 2, 0, 1, 2, 3, 4, 1, 4, 2,
## 3, 6, 0, 4, 0, 3, 3, 4, 2, 3, 3, 3, 4, 4, 4, 3, 4, 3, 5, 2, 6,
## 4, 3, 4, 5, 1, 5, 5, 4, 2, 4, 4, 0, 3, 4, 3, 5, 3, 6, 3, 5, 3,
## 2, 2, 1, 2, 4, 0, 5, 4, 3, 3, 1, 4, 1, 0, 3, 3, 7, 7, 0, 4, 5,
## 4, 6, 4, 5, 4, 4, 2, 2, 2, 4, 4, 3, 6, 1, 5, 5, 6, 4, 1, 5, 5,
## 4, 2, 2, 4, 5, 4, 4, 0, 1, 3, 3, 2, 5, 2, 1, 2, 3, 2, 5, 2, 4,
## 4, 4, 4, 4, 3, 3, 4, 3, 4, 3, 3, 4, 5, 4, 7, 5, 4, 4, 4, 3, 4,
## 4, 3, 3, 4, 6, 6, 3, 4, 4, 4, 0, 2, 3, 5, 2, 2, 6, 3, 4, 3, 5,
## 3, 0, 2, 4, 7, 6, 1, 5, 2, 7, 2, 2, 2, 0, 3, 3, 6, 3, 3, 0, 2,
## 3, 4, 4, 2, 8, 0, 4, 4, 4, 7, 5, 2, 3, 1, 1, 1, 4, 5, 3, 5, 3,
## 0, 4, 1, 4, 4, 3, 4, 1, 7, 2, 5, 0, 2, 3, 4, 1, 0, 1, 0, 2, 5,
## 4, 3, 2, 6, 0, 3, 0, 7, 3, 3, 3, 3, 3, 3, 5, 4, 2, 6, 2, 0, 4,
## 4, 4, 3, 2, 4, 5, 3, 3, 2, 0, 0, 4, 2, 3, 3, 1, 0, 4, 3, 3, 4,
## 6, 2, 1, 4, 4, 3, 5, 7, 2, 3, 6, 8, 4, 3, 1, 4, 3, 2, 0, 3, 3,
## 3, 3, 4, 0, 5, 4, 6, 3, 1, 6, 5, 2, 5, 3, 4, 2, 4, 2, 3, 1, 4,
## 4, 2, 3, 4, 3, 4, 2, 3, 3, 3, 4, 3, 4, 3, 5, 2, 4, 7, 1, 4, 3,
## 2, 4, 4, 2, 3, 7, 2, 2, 4, 4, 3, 3, 3, 2, 5, 2, 2, 2, 4, 3, 0,
## 0, 5, 1, 5, 3, 2, 4, 6, 3, 3, 3, 1, 0, 3, 4, 9, 5, 2, 3, 5, 5,
## 3, 4, 4, 5, 3, 4, 4, 3, 4, 2, 3, 8, 3, 3, 1, 2, 3, 4, 4, 3, 0,
## 3, 3, 3, 2, 4, 2, 4, 2, 6, 1, 6, 3, 4, 2, 6, 6, 4, 2, 4, 4, 4,
## 4, 4, 5, 4, 3, 5, 3, 4, 6, 0, 7, 2, 4, 7, 6, 0, 0, 5, 4, 4, 4,
## 4, 3, 1, 3, 4, 4, 2, 3, 6, 5, 0, 4, 4, 0, 0, 4, 0, 2, 3, 3, 3,
## 2, 4, 4, 4, 7, 3, 4, 0, 0, 2, 3, 4, 4, 7, 4, 6, 2, 3, 2, 2, 1,
## 3, 3, 1, 0, 4, 5, 3, 2, 6, 2, 4, 2, 3, 5, 7, 9, 5, 6, 3, 4, 0,
## 2, 4, 2, 4, 4, 5, 3, 3, 1, 1, 4, 3, 1, 2, 3, 4, 3, 2, 3, 6, 3,
## 5, 1, 4, 7, 4, 3, 7, 5, 2, 3, 5, 5, 4, 6, 9, 4, 2, 5, 4, 2, 5,
## 3, 3, 2, 3, 3, 6, 3, 1, 4, 0, 5, 3, 3, 3, 5, 4, 1, 3, 5, 0, 0,
## 3, 3, 0, 1, 4, 3, 2, 0, 4, 4, 6, 4, 9, 5, 0, 3, 3, 6, 2, 4, 2,
## 3, 4, 2, 1, 3, 6, 4, 6, 1, 6, 2, 5, 7, 4, 6, 4, 1, 5, 0, 5, 0,
## 2, 3, 5, 2, 6, 3, 3, 6, 5, 7, 0, 3, 3, 3, 0, 0, 4, 2, 1, 5, 4,
## 4, 3, 5), c(7, 4, 4, 2, 0, 4, 5, 6, 8, 5, 3, 1, 5, 4, 2, 6, 2,
## 7, 1, 9, 9, 7, 1, 7, 2, 6, 2, 7, 9, 7, 3, 0, 6, 5, 2, 2, 0, 6,
## 6, 8, 9, 4, 3, 6, 5, 6, 5, 5, 4, 7, 7, 4, 6, 3, 7, 5, 1, 4, 6,
## 5, 3, 6, 3, 2, 2, 4, 6, 2, 2, 8, 2, 4, 5, 3, 0, 5, 6, 0, 3, 3,
## 5, 9, 2, 6, 5, 5, 5, 4, 2, 8, 3, 0, 5, 7, 2, 5, 9, 0, 4, 5, 8,
## 0, 4, 4, 4, 9, 0, 2, 4, 9, 2, 4, 6, 0, 5, 5, 6, 5, 0, 6, 7, 9,
## 7, 6, 2, 7, 3, 0, 4, 2, 2, 5, 7, 4, 0, 5, 7, 6, 5, 2, 3, 2, 3,
## 0, 8, 8, 6, 2, 3, 3, 1, 1, 6, 2, 2, 5, 3, 6, 7, 4, 6, 7, 8, 3,
## 5, 8, 6, 3, 5, 6, 5, 4, 7, 7, 5, 7, 3, 1, 8, 5, 2, 4, 5, 0, 7,
## 5, 3, 4, 4, 2, 3, 5, 9, 6, 9, 4, 2, 6, 6, 4, 5, 6, 2, 2, 4, 1,
## 3, 5, 8, 3, 2, 9, 3, 7, 5, 5, 6, 3, 4, 4, 6, 2, 6, 4, 5, 5, 3,
## 6, 6, 3, 4, 4, 4, 9, 7, 2, 9, 7, 5, 2, 3, 3, 9, 4, 5, 2, 1, 9,
## 6, 7, 6, 2, 3, 5, 6, 6, 1, 8, 3, 5, 4, 2, 1, 9, 5, 7, 5, 9, 3,
## 7, 9, 2, 4, 4, 5, 6, 5, 1, 2, 5, 7, 5, 2, 5, 4, 4, 3, 4, 5, 6,
## 7, 4, 5, 3, 0, 2, 7, 2, 7, 1, 9, 3, 6, 4, 4, 4, 6, 9, 2, 5, 6,
## 2, 5, 2, 4, 1, 8, 2, 6, 3, 6, 2, 6, 2, 9, 4, 3, 5, 4, 2, 7, 3,
## 6, 4, 0, 4, 3, 6, 6, 3, 2, 8, 7, 5, 6, 6, 7, 2, 9, 4, 3, 5, 3,
## 8, 4, 2, 5, 6, 7, 6, 7, 4, 4, 6, 3, 6, 5, 2, 1, 4, 0, 6, 0, 3,
## 2, 5, 6, 4, 9, 7, 9, 8, 7, 6, 2, 1, 3, 7, 5, 1, 5, 5, 9, 5, 3,
## 2, 6, 4, 5, 6, 5, 5, 0, 4, 4, 5, 4, 2, 3, 4, 5, 5, 0, 0, 3, 2,
## 0, 4, 4, 4, 9, 5, 2, 5, 2, 5, 3, 6, 3, 4, 7, 7, 8, 7, 5, 9, 3,
## 4, 5, 0, 2, 4, 1, 9, 4, 6, 2, 0, 9, 5, 4, 3, 0, 4, 1, 5, 4, 7,
## 6, 4, 2, 2, 5, 3, 7, 4, 5, 3, 2, 8, 4, 4, 5, 6, 7, 2, 3, 5, 4,
## 9, 8, 5, 4, 7, 2, 7, 8, 7, 6, 7, 5, 5, 4, 2, 5, 3, 2, 6, 4, 4,
## 6, 5, 4, 6, 3, 4, 4, 2, 4, 4, 2, 4, 6, 4, 3, 5, 6, 5, 3, 3, 6,
## 5, 3, 5, 9, 7, 0, 2, 7, 7, 2, 6, 4, 6, 3, 6, 2, 7, 0, 0, 3, 8,
## 4, 6, 0, 6, 7, 7, 0, 2, 5, 3, 3, 4, 8, 7, 6, 4, 5, 6, 1, 9, 5,
## 5, 4, 0, 4, 7, 6, 8, 6, 8, 5, 3, 1, 3, 2, 9, 3, 7, 4, 5, 5, 4,
## 1, 0, 6, 4, 9, 6, 5, 0, 8, 9, 1, 4, 7, 1, 5, 5, 2, 3, 9, 5, 9,
## 1, 6, 6, 5, 6, 6, 4, 4, 3, 7, 3, 7, 9, 5, 4, 4, 5, 8, 5, 3, 6,
## 4, 7, 9, 9, 3, 7, 5, 6, 8, 9, 5, 2, 2, 4, 2, 7, 7, 5, 6, 2, 3,
## 2, 0, 6, 3, 1, 5, 5, 8, 4, 6, 7, 2, 6, 5, 2, 5, 4, 9, 2, 3, 0,
## 6, 8, 2, 0, 7, 1, 5, 5, 7, 5, 4, 4, 5, 5, 5, 7, 2, 4, 5, 5, 6,
## 6, 6, 3, 4, 5, 5, 2, 2, 7, 4, 0, 8, 5, 2, 4, 5, 2, 7, 6, 0, 7,
## 7, 5, 5, 5, 6, 2, 7, 1, 7, 5, 7, 5, 5, 9, 9, 4, 8, 4, 2, 8, 3,
## 3, 6, 5, 5, 8, 9, 6, 2, 0, 3, 2, 6, 4, 4, 6, 5, 0, 4, 4, 2, 3,
## 6, 3, 7, 5, 0, 4, 6, 8, 7, 6, 4, 4, 6, 7, 6, 1, 6, 6, 5, 7, 2,
## 6, 3, 8, 2, 4, 3, 6, 3, 3, 4, 7, 2, 4, 2, 4, 2, 4, 5, 5, 2, 3,
## 5, 3, 9, 2, 2, 2, 0, 3, 9, 5, 1, 4, 5, 5, 5, 4, 3, 2, 4, 5, 4,
## 2, 3, 3, 9, 2, 5, 9, 7, 3, 9, 4, 6, 5, 6, 6, 5, 5, 4, 2, 6, 5,
## 9, 5, 6, 5, 5, 3, 2, 5, 0, 7, 1, 7, 7, 8, 5, 4, 8, 9, 5, 1, 2,
## 7, 3, 4, 5, 5, 4, 3, 2, 0, 2, 2, 4, 5, 9, 7, 5, 6, 5, 3, 3, 6,
## 0, 4, 8, 5, 5, 8, 7, 5, 4, 5, 7, 5, 3, 5, 0, 6, 5, 0, 0, 6, 2,
## 1, 7, 6, 4, 2, 5, 3, 0, 5, 4, 1, 5, 0, 4, 6, 3, 4, 6, 6, 3, 2,
## 8, 5, 9, 4, 6, 5, 6, 1, 5, 0, 6, 3, 9, 8, 6, 6, 9, 7, 4, 5, 5,
## 4, 5, 3, 3, 5, 0, 4, 9, 5, 6, 2, 6, 5, 7, 6, 5, 7, 2, 3, 1, 4,
## 3, 8, 3, 7, 4, 2, 4, 2, 4, 5, 2, 5, 4, 9, 7, 6, 1, 7, 3, 2, 6,
## 3, 0, 0, 9, 6, 5, 6, 9, 9, 5, 7, 8, 4, 2, 5, 4, 4), c(1, 0, 0,
## 4, 0, 2, 0, 2, 1, 2, 0, 4, 1, 3, 1, 2, 2, 0, 6, 0, 0, 0, 6, 0,
## 4, 1, 1, 2, 0, 0, 2, 3, 3, 2, 4, 2, 2, 2, 2, 0, 2, 5, 3, 2, 2,
## 2, 2, 1, 1, 0, 0, 1, 1, 4, 1, 0, 2, 1, 1, 3, 1, 1, 2, 0, 0, 3,
## 1, 7, 2, 1, 2, 3, 1, 4, 2, 1, 1, 4, 6, 1, 1, 4, 6, 1, 0, 2, 4,
## 2, 2, 1, 1, 7, 1, 0, 1, 3, 0, 4, 1, 1, 1, 4, 3, 4, 4, 0, 0, 3,
## 0, 0, 3, 2, 2, 4, 1, 5, 2, 1, 0, 0, 1, 0, 0, 1, 2, 0, 3, 7, 1,
## 1, 3, 2, 0, 5, 3, 3, 2, 0, 4, 6, 2, 3, 0, 1, 1, 0, 0, 7, 1, 4,
## 3, 6, 0, 2, 2, 1, 1, 1, 0, 1, 1, 2, 3, 2, 2, 1, 4, 2, 4, 0, 1,
## 4, 2, 1, 0, 2, 2, 2, 1, 1, 4, 2, 0, 0, 2, 1, 0, 3, 3, 3, 1, 1,
## 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 5, 4, 2, 1, 5, 1, 0, 4, 1, 0, 3,
## 0, 1, 3, 0, 1, 2, 3, 0, 1, 1, 1, 1, 1, 3, 1, 2, 3, 3, 4, 2, 0,
## 0, 3, 0, 0, 0, 3, 3, 3, 0, 2, 0, 2, 6, 0, 2, 5, 2, 2, 1, 1, 1,
## 4, 1, 0, 2, 1, 3, 7, 4, 0, 1, 1, 2, 0, 3, 1, 5, 0, 3, 0, 5, 0,
## 2, 1, 1, 1, 0, 0, 2, 4, 0, 1, 2, 6, 2, 2, 0, 2, 3, 3, 0, 1, 0,
## 3, 0, 1, 0, 3, 1, 4, 3, 0, 0, 0, 7, 2, 5, 0, 2, 7, 3, 6, 1, 3,
## 1, 2, 0, 2, 1, 4, 5, 3, 0, 2, 2, 1, 1, 1, 1, 2, 4, 2, 0, 1, 2,
## 3, 1, 1, 0, 2, 0, 0, 0, 6, 0, 1, 2, 3, 3, 1, 2, 1, 0, 0, 2, 1,
## 0, 3, 0, 1, 2, 5, 0, 3, 1, 3, 4, 1, 0, 1, 3, 0, 2, 2, 0, 0, 0,
## 1, 0, 2, 3, 2, 3, 1, 2, 2, 2, 0, 0, 1, 2, 3, 1, 3, 1, 0, 0, 3,
## 0, 2, 2, 1, 5, 6, 4, 3, 2, 0, 5, 9, 2, 2, 3, 3, 2, 1, 0, 3, 5,
## 2, 3, 2, 1, 0, 1, 6, 0, 1, 0, 0, 0, 5, 2, 2, 3, 6, 7, 1, 6, 0,
## 3, 2, 0, 2, 0, 2, 3, 3, 1, 3, 7, 2, 2, 0, 1, 4, 3, 4, 2, 1, 1,
## 2, 3, 1, 2, 1, 2, 0, 1, 2, 2, 7, 0, 0, 2, 0, 0, 2, 2, 1, 2, 1,
## 1, 0, 5, 1, 3, 0, 2, 3, 2, 3, 2, 0, 3, 3, 0, 0, 3, 0, 3, 0, 2,
## 2, 0, 2, 3, 3, 3, 2, 3, 2, 0, 1, 1, 3, 0, 2, 3, 1, 0, 1, 6, 2,
## 1, 1, 3, 1, 2, 2, 4, 0, 3, 0, 5, 2, 4, 1, 2, 1, 2, 2, 1, 0, 3,
## 8, 1, 0, 0, 3, 2, 0, 2, 2, 1, 1, 3, 0, 0, 0, 2, 2, 0, 0, 0, 0,
## 2, 0, 1, 0, 7, 5, 4, 5, 1, 0, 3, 4, 2, 6, 3, 2, 1, 0, 0, 2, 2,
## 0, 0, 3, 5, 0, 0, 5, 0, 1, 2, 1, 0, 2, 0, 3, 0, 0, 2, 4, 2, 2,
## 0, 2, 2, 3, 0, 0, 0, 3, 1, 2, 0, 1, 2, 1, 3, 1, 0, 0, 2, 0, 3,
## 2, 4, 0, 0, 5, 7, 2, 1, 0, 0, 2, 1, 7, 2, 3, 9, 1, 4, 1, 2, 1,
## 1, 2, 0, 2, 3, 0, 2, 3, 3, 6, 0, 3, 3, 3, 0, 1, 0, 9, 0, 5, 1,
## 1, 1, 1, 3, 6, 4, 2, 1, 0, 5, 3, 1, 1, 3, 0, 2, 4, 2, 2, 0, 7,
## 5, 2, 3, 2, 0, 1, 5, 3, 1, 4, 4, 2, 2, 1, 0, 2, 0, 2, 2, 8, 0,
## 6, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 5, 0, 2, 3, 0, 2, 1, 0, 0, 0,
## 5, 1, 1, 2, 0, 2, 3, 1, 4, 0, 3, 3, 0, 4, 0, 2, 0, 2, 3, 2, 2,
## 1, 0, 2, 2, 2, 0, 5, 2, 6, 0, 1, 1, 1, 3, 1, 0, 2, 0, 4, 5, 4,
## 4, 0, 1, 1, 6, 2, 4, 1, 2, 0, 0, 2, 2, 3, 2, 5, 2, 5, 3, 7, 2,
## 0, 0, 2, 3, 2, 0, 2, 0, 3, 7, 6, 2, 0, 3, 3, 0, 4, 2, 4, 3, 0,
## 5, 2, 0, 6, 0, 1, 0, 0, 1, 0, 3, 0, 0, 0, 0, 2, 1, 0, 4, 3, 2,
## 0, 4, 1, 6, 0, 1, 1, 1, 2, 1, 0, 2, 2, 3, 0, 0, 1, 4, 2, 2, 1,
## 0, 0, 2, 1, 4, 1, 0, 1, 1, 3, 0, 3, 3, 3, 0, 1, 0, 1, 2, 1, 0,
## 1, 2, 2, 1, 2, 3, 1, 9, 2, 2, 2, 4, 2, 0, 7, 4, 1, 0, 5, 1, 1,
## 1, 0, 2, 6, 2, 9, 2, 2, 0, 4, 1, 0, 2, 6, 1, 3, 0, 0, 0, 0, 0,
## 6, 1, 9, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 3, 0, 2, 1, 2, 1, 4, 2,
## 0, 1, 1, 2, 0, 0, 0, 2, 1, 0, 7, 2, 2, 0, 2, 0, 0, 0, 0, 3, 0,
## 0, 1, 1, 2, 2, 3, 0, 4, 5, 3, 0, 3, 6, 1, 0, 9, 2, 0, 2, 2, 3,
## 0, 0, 0, 1, 0, 2, 7, 2, 3, 0), c(0, 0, 0, 0, 5, 0, 0, 0, 1, 0,
## 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 5, 1, 0, 0, 1, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1,
## 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 5, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1,
## 0, 2, 2, 0, 0, 0, 1, 2, 0, 0, 0, 5, 0, 0, 1, 0, 1, 0, 1, 0, 0,
## 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0,
## 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0,
## 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 0, 0, 0,
## 0, 1, 1, 0, 0, 5, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0,
## 2, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 1, 5, 0, 1, 1, 0, 1, 0,
## 1, 1, 0, 4, 0, 0, 1, 5, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1,
## 3, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 2,
## 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 2,
## 0, 5, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0,
## 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 2, 1, 5, 0, 0, 0, 0, 2, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0,
## 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 5, 0, 1,
## 1, 1, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
## 3, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 0, 0, 1, 0,
## 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 5, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,
## 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 5, 2, 0, 1, 1, 0,
## 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1,
## 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
## 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 0, 2,
## 0, 0, 0, 0, 3, 1, 0, 0, 2, 0, 0, 0, 0, 2, 3, 2, 0, 2, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 0), c(1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 3, 2, 0, 0, 0, 1, 0, 5, 2, 1, 0, 0, 1, 0, 0, 0, 0, 2,
## 0, 0, 1, 0, 1, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2,
## 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,
## 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 1, 5,
## 2, 0, 0, 1, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 1,
## 2, 0, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0,
## 0, 2, 1, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 2, 0, 0, 1, 1, 0, 2, 0,
## 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0,
## 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 3, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 1, 2, 0,
## 0, 0, 0, 0, 0, 1, 5, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 4, 1,
## 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
## 0, 1, 2, 1, 0, 0, 3, 4, 0, 1, 1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0,
## 0, 1, 1, 0, 0, 0, 1, 0, 5, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2,
## 1, 0, 0, 0, 3, 2, 0, 0, 2, 0, 0, 5, 0, 2, 0, 1, 0, 0, 0, 0, 2,
## 0, 0, 1, 0, 0, 0, 0, 2, 0, 5, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0,
## 0, 0, 1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 4, 1, 0,
## 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 1, 1, 1, 0, 3, 0, 1,
## 2, 0, 2, 0, 0, 3, 3, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1,
## 3, 0, 2, 0, 0, 1, 1, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 2, 0, 1, 1, 0, 2, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0,
## 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0,
## 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1,
## 0, 0, 1, 0, 1, 0, 0, 0, 2, 1, 2, 1, 5, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 5, 0,
## 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0), c(2, 5, 7,
## 3, 0, 4, 4, 2, 1, 3, 9, 5, 3, 2, 4, 2, 4, 1, 3, 2, 0, 4, 2, 2,
## 3, 4, 5, 0, 0, 2, 5, 1, 2, 3, 3, 3, 7, 3, 2, 1, 2, 4, 3, 2, 3,
## 2, 3, 2, 6, 3, 3, 4, 3, 0, 3, 6, 4, 5, 4, 4, 5, 2, 5, 7, 3, 4,
## 3, 0, 4, 1, 4, 4, 5, 4, 5, 3, 2, 1, 1, 6, 6, 2, 3, 4, 4, 3, 2,
## 3, 4, 3, 4, 2, 4, 2, 3, 2, 4, 5, 3, 3, 2, 4, 4, 2, 0, 0, 0, 2,
## 7, 0, 5, 4, 2, 3, 4, 4, 3, 3, 6, 0, 2, 0, 2, 3, 5, 0, 4, 2, 4,
## 3, 5, 3, 2, 4, 6, 4, 1, 2, 2, 2, 3, 4, 4, 4, 1, 1, 3, 2, 3, 4,
## 4, 2, 2, 4, 5, 3, 5, 3, 4, 6, 2, 3, 0, 0, 0, 1, 2, 2, 3, 3, 2,
## 2, 2, 3, 5, 3, 4, 4, 2, 2, 3, 3, 4, 5, 1, 3, 7, 2, 2, 4, 1, 3,
## 2, 2, 2, 0, 7, 0, 3, 7, 3, 0, 1, 2, 2, 4, 4, 4, 0, 0, 4, 0, 5,
## 5, 3, 1, 5, 5, 5, 2, 4, 6, 4, 5, 3, 3, 3, 3, 4, 4, 3, 3, 4, 0,
## 2, 5, 0, 2, 4, 5, 4, 4, 0, 3, 6, 3, 2, 2, 2, 2, 2, 2, 3, 5, 4,
## 0, 4, 4, 2, 2, 0, 2, 4, 2, 4, 2, 3, 0, 4, 2, 0, 3, 4, 2, 4, 0,
## 4, 5, 6, 3, 0, 4, 6, 2, 3, 1, 3, 2, 3, 1, 2, 3, 2, 3, 0, 3, 0,
## 4, 3, 4, 0, 4, 3, 1, 2, 4, 0, 0, 0, 3, 1, 3, 3, 0, 2, 3, 2, 4,
## 2, 4, 0, 2, 4, 3, 0, 2, 9, 1, 3, 4, 3, 6, 3, 5, 5, 2, 7, 3, 3,
## 4, 6, 1, 0, 0, 3, 0, 2, 3, 0, 5, 2, 2, 5, 1, 2, 6, 9, 9, 1, 1,
## 2, 3, 3, 2, 5, 0, 2, 6, 4, 2, 4, 3, 0, 2, 4, 9, 4, 3, 0, 2, 0,
## 2, 2, 2, 4, 6, 4, 3, 4, 4, 4, 4, 9, 2, 2, 5, 4, 2, 2, 2, 2, 1,
## 0, 5, 4, 2, 4, 1, 2, 3, 3, 2, 0, 0, 5, 5, 0, 2, 3, 5, 1, 2, 3,
## 3, 4, 3, 3, 7, 2, 2, 1, 2, 2, 0, 2, 0, 5, 4, 1, 2, 0, 5, 2, 2,
## 2, 1, 7, 7, 0, 3, 2, 4, 4, 2, 2, 3, 2, 2, 3, 2, 4, 2, 2, 6, 3,
## 4, 1, 4, 4, 2, 3, 7, 2, 2, 1, 0, 6, 2, 2, 2, 4, 3, 6, 2, 6, 2,
## 1, 0, 2, 2, 1, 4, 2, 4, 3, 4, 4, 9, 1, 2, 5, 3, 2, 2, 3, 5, 4,
## 4, 1, 0, 5, 3, 2, 3, 4, 3, 4, 2, 4, 3, 3, 4, 3, 3, 2, 1, 2, 7,
## 3, 3, 3, 2, 2, 2, 2, 3, 0, 2, 2, 7, 4, 2, 3, 3, 7, 2, 1, 0, 3,
## 0, 2, 6, 6, 2, 4, 1, 2, 2, 4, 2, 4, 0, 4, 4, 3, 7, 0, 2, 4, 3,
## 3, 4, 3, 5, 1, 2, 3, 0, 1, 2, 3, 1, 4, 2, 4, 7, 2, 5, 3, 3, 4,
## 0, 4, 3, 1, 9, 2, 2, 2, 2, 5, 3, 0, 3, 0, 4, 0, 2, 5, 0, 1, 5,
## 5, 5, 1, 2, 2, 0, 6, 2, 6, 4, 1, 2, 5, 3, 2, 2, 0, 0, 5, 0, 3,
## 2, 2, 1, 3, 3, 0, 3, 4, 5, 1, 2, 1, 0, 4, 3, 0, 3, 4, 5, 3, 5,
## 1, 2, 3, 1, 0, 3, 3, 4, 1, 3, 0, 2, 4, 3, 3, 3, 4, 0, 3, 2, 6,
## 4, 3, 2, 5, 3, 2, 3, 4, 2, 2, 2, 7, 3, 1, 3, 2, 2, 2, 2, 4, 0,
## 1, 2, 2, 7, 2, 3, 3, 5, 3, 3, 0, 2, 7, 3, 2, 2, 5, 2, 2, 0, 0,
## 2, 1, 3, 2, 4, 2, 0, 0, 4, 1, 5, 2, 1, 4, 5, 5, 4, 2, 4, 2, 3,
## 3, 3, 6, 5, 2, 5, 0, 3, 3, 0, 2, 4, 3, 3, 3, 5, 0, 3, 1, 3, 3,
## 4, 2, 2, 3, 3, 2, 2, 2, 2, 3, 4, 3, 2, 4, 3, 3, 2, 4, 2, 2, 2,
## 4, 4, 2, 3, 2, 4, 3, 2, 4, 7, 5, 3, 3, 6, 2, 5, 3, 3, 3, 0, 7,
## 7, 0, 4, 4, 7, 2, 1, 4, 3, 2, 2, 0, 5, 5, 5, 9, 2, 3, 2, 1, 4,
## 2, 4, 2, 1, 3, 6, 2, 2, 3, 3, 2, 7, 7, 3, 2, 2, 4, 5, 4, 4, 4,
## 2, 4, 4, 2, 8, 6, 1, 6, 3, 1, 0, 3, 4, 5, 2, 3, 4, 3, 4, 3, 5,
## 7, 0, 3, 6, 2, 3, 2, 3, 3, 2, 9, 4, 3, 0, 6, 4, 3, 2, 3, 1, 4,
## 3, 2, 4, 1, 4, 2, 3, 0, 3, 2, 7, 2, 2, 7, 2, 2, 3, 0, 1, 1, 4,
## 3, 2, 3, 2, 3, 0, 4, 2, 6, 2, 3, 2, 0, 2, 1, 3, 0, 0, 5, 5, 0,
## 2, 4, 0, 2, 5, 2, 4, 9, 1, 0, 3, 2, 3, 4, 9, 3, 1, 3, 3, 2, 3,
## 0, 2, 3, 6, 2, 3, 2, 2, 3, 3, 0, 2, 6, 5, 3, 1, 4, 0, 4, 3, 4,
## 4, 4, 4, 3, 4, 0, 2, 0, 0, 5, 2, 3, 3, 2, 1, 0, 7, 2, 3, 4, 0,
## 0, 3, 2, 1, 2, 7, 0, 3, 2, 2), c(5, 0, 0, 1, 0, 2, 1, 5, 8, 3,
## 0, 1, 2, 2, 3, 5, 0, 1, 0, 4, 6, 0, 0, 4, 3, 2, 2, 2, 3, 6, 3,
## 1, 4, 2, 3, 1, 0, 2, 5, 6, 3, 0, 2, 2, 2, 3, 3, 0, 1, 6, 4, 2,
## 2, 4, 3, 3, 3, 2, 1, 1, 2, 4, 2, 0, 0, 1, 2, 2, 0, 4, 0, 1, 3,
## 1, 1, 2, 2, 4, 1, 1, 1, 2, 1, 2, 3, 2, 2, 5, 1, 6, 2, 0, 2, 4,
## 3, 2, 5, 1, 1, 1, 6, 2, 1, 0, 2, 4, 0, 2, 0, 5, 2, 2, 5, 0, 2,
## 1, 3, 5, 3, 3, 3, 5, 4, 4, 0, 5, 1, 0, 2, 2, 2, 1, 4, 0, 0, 2,
## 4, 4, 2, 2, 3, 2, 3, 4, 6, 5, 3, 0, 0, 1, 1, 0, 2, 0, 2, 3, 3,
## 2, 0, 1, 2, 3, 2, 0, 4, 0, 2, 0, 3, 2, 3, 0, 1, 3, 1, 3, 2, 2,
## 2, 3, 2, 2, 5, 0, 4, 0, 0, 3, 2, 2, 4, 5, 4, 4, 7, 5, 0, 6, 3,
## 0, 2, 3, 1, 2, 5, 2, 0, 3, 6, 1, 1, 5, 1, 0, 3, 0, 4, 3, 2, 3,
## 3, 1, 2, 1, 1, 3, 2, 3, 3, 1, 2, 2, 3, 3, 7, 1, 0, 4, 4, 2, 1,
## 1, 3, 3, 3, 4, 2, 7, 5, 0, 3, 0, 2, 1, 2, 3, 1, 0, 0, 3, 0, 0,
## 0, 7, 4, 4, 3, 7, 1, 4, 0, 5, 3, 2, 0, 3, 0, 2, 1, 2, 0, 1, 1,
## 2, 2, 1, 5, 2, 3, 5, 4, 0, 5, 2, 0, 2, 0, 2, 1, 2, 6, 1, 3, 4,
## 2, 2, 3, 5, 2, 2, 0, 4, 2, 2, 3, 0, 2, 1, 4, 2, 3, 2, 2, 1, 5,
## 2, 0, 5, 4, 1, 4, 2, 0, 2, 0, 3, 0, 3, 2, 1, 1, 0, 6, 5, 4, 3,
## 4, 1, 5, 4, 2, 2, 0, 0, 2, 1, 0, 0, 5, 3, 4, 2, 2, 4, 2, 0, 5,
## 0, 2, 2, 0, 3, 0, 1, 2, 0, 0, 3, 7, 3, 5, 2, 4, 5, 1, 2, 1, 3,
## 2, 1, 1, 3, 0, 3, 3, 2, 2, 3, 3, 6, 2, 2, 0, 1, 2, 3, 0, 1, 2,
## 2, 1, 4, 0, 0, 1, 2, 3, 4, 1, 2, 5, 2, 1, 2, 2, 3, 3, 0, 2, 0,
## 2, 2, 4, 0, 2, 0, 0, 2, 2, 0, 1, 2, 2, 3, 3, 3, 0, 0, 3, 4, 0,
## 1, 2, 2, 0, 4, 2, 7, 2, 2, 0, 1, 3, 2, 3, 4, 0, 1, 3, 2, 2, 0,
## 0, 4, 4, 2, 0, 4, 0, 5, 0, 2, 2, 2, 1, 4, 0, 3, 0, 0, 0, 5, 0,
## 0, 3, 2, 3, 0, 4, 2, 1, 6, 2, 8, 0, 4, 2, 0, 8, 2, 2, 2, 5, 3,
## 1, 2, 3, 4, 1, 2, 3, 2, 2, 5, 7, 5, 0, 0, 4, 4, 1, 1, 2, 3, 0,
## 3, 0, 4, 0, 0, 0, 6, 0, 2, 0, 2, 5, 9, 1, 0, 4, 0, 0, 3, 1, 2,
## 2, 2, 3, 4, 1, 3, 2, 2, 4, 0, 5, 6, 3, 0, 3, 0, 4, 2, 1, 2, 1,
## 0, 4, 4, 2, 4, 2, 2, 3, 0, 4, 4, 6, 2, 3, 0, 0, 2, 1, 0, 4, 1,
## 5, 3, 0, 0, 3, 2, 4, 1, 5, 4, 0, 3, 3, 1, 2, 2, 3, 0, 4, 5, 3,
## 2, 1, 2, 4, 3, 0, 3, 3, 4, 3, 5, 2, 3, 2, 5, 2, 5, 4, 1, 2, 1,
## 2, 0, 1, 4, 1, 2, 3, 0, 0, 2, 0, 2, 3, 3, 6, 1, 4, 3, 0, 6, 3,
## 2, 3, 1, 5, 2, 1, 0, 3, 6, 2, 0, 6, 2, 1, 3, 4, 4, 2, 0, 2, 3,
## 1, 1, 1, 2, 2, 1, 0, 0, 0, 1, 2, 3, 4, 2, 0, 4, 2, 0, 4, 2, 1,
## 2, 2, 1, 0, 5, 0, 3, 3, 4, 2, 3, 4, 0, 3, 0, 2, 3, 3, 3, 1, 2,
## 0, 5, 5, 1, 2, 4, 2, 0, 1, 3, 3, 0, 4, 3, 1, 3, 1, 0, 5, 2, 5,
## 2, 3, 0, 3, 1, 5, 1, 3, 2, 0, 3, 1, 3, 4, 1, 4, 5, 3, 5, 2, 0,
## 3, 1, 2, 2, 2, 1, 2, 3, 2, 6, 0, 0, 2, 2, 0, 5, 3, 3, 1, 1, 1,
## 3, 3, 0, 2, 2, 3, 0, 4, 0, 3, 2, 1, 2, 0, 0, 6, 1, 1, 1, 2, 5,
## 2, 1, 0, 2, 1, 4, 2, 1, 0, 0, 3, 0, 5, 0, 0, 2, 4, 1, 4, 1, 8,
## 6, 2, 6, 2, 0, 0, 6, 4, 3, 2, 2, 1, 2, 0, 4, 2, 4, 1, 0, 2, 6,
## 1, 3, 2, 5, 1, 3, 1, 4, 2, 1, 3, 3, 4, 3, 0, 0, 1, 1, 4, 2, 3,
## 4, 2, 2, 0, 1, 1, 0, 3, 1, 0, 0, 1, 3, 4, 3, 0, 2, 5, 2, 0, 3,
## 0, 3, 5, 0, 1, 3, 0, 0, 0, 3, 5, 1, 3, 1, 3, 5, 2, 0, 2, 0, 3,
## 3, 0, 2, 4, 0, 0, 2, 8, 4, 5, 5, 3, 2, 3, 0, 3, 0, 5, 1, 4, 1,
## 0, 3, 3, 3, 2, 2, 3, 0, 2, 4, 2, 5, 1, 3, 6, 3, 3, 1, 6, 6, 4,
## 4, 4, 4, 1, 3, 1, 4, 2, 7, 3, 3, 1, 0, 2, 0, 4, 3, 1, 0, 5, 7,
## 0, 0, 1, 6, 2, 1, 3, 4, 0, 0, 4, 4, 2, 0, 5, 6, 4, 0, 4, 0, 2,
## 2, 3, 6), c(2, 4, 2, 2, 0, 2, 5, 2, 1, 3, 0, 1, 4, 2, 2, 2, 4,
## 5, 1, 4, 0, 3, 1, 2, 0, 4, 2, 0, 5, 1, 0, 5, 1, 3, 0, 3, 0, 3,
## 2, 3, 2, 1, 2, 2, 3, 3, 2, 7, 3, 0, 3, 3, 4, 1, 4, 0, 2, 1, 4,
## 2, 1, 2, 1, 2, 6, 1, 4, 0, 2, 5, 2, 2, 1, 0, 1, 5, 5, 0, 3, 2,
## 3, 1, 0, 4, 3, 3, 0, 0, 3, 0, 3, 0, 4, 2, 3, 1, 0, 0, 4, 5, 2,
## 0, 1, 4, 3, 5, 0, 2, 2, 4, 1, 2, 2, 3, 2, 0, 2, 2, 0, 5, 4, 4,
## 2, 2, 2, 4, 2, 1, 3, 4, 1, 4, 4, 0, 0, 2, 2, 3, 0, 1, 3, 1, 2,
## 1, 3, 4, 4, 1, 0, 0, 2, 1, 6, 4, 1, 2, 1, 3, 5, 3, 5, 2, 4, 3,
## 3, 7, 1, 4, 0, 4, 4, 4, 2, 4, 4, 3, 2, 2, 5, 1, 1, 2, 0, 4, 2,
## 5, 2, 1, 1, 2, 4, 2, 4, 2, 0, 4, 2, 3, 2, 0, 3, 5, 3, 3, 0, 3,
## 0, 1, 0, 4, 3, 4, 2, 4, 3, 1, 0, 1, 2, 1, 2, 3, 4, 3, 6, 2, 1,
## 3, 2, 2, 2, 0, 0, 5, 0, 1, 9, 3, 1, 1, 2, 2, 0, 3, 0, 0, 1, 0,
## 2, 3, 3, 0, 4, 3, 4, 3, 4, 5, 4, 3, 3, 0, 1, 0, 2, 4, 3, 2, 2,
## 2, 4, 1, 0, 6, 0, 5, 4, 2, 3, 4, 9, 5, 1, 2, 2, 2, 1, 0, 2, 1,
## 2, 4, 1, 0, 0, 4, 9, 1, 5, 3, 0, 2, 2, 2, 1, 3, 5, 4, 0, 3, 4,
## 3, 3, 0, 3, 1, 5, 3, 2, 2, 5, 4, 4, 1, 0, 3, 0, 2, 1, 3, 2, 2,
## 4, 1, 0, 3, 2, 2, 3, 2, 2, 8, 0, 3, 1, 5, 2, 0, 4, 1, 3, 1, 2,
## 7, 4, 2, 0, 0, 2, 2, 2, 2, 2, 2, 1, 5, 2, 2, 3, 3, 2, 3, 0, 5,
## 1, 0, 3, 2, 2, 4, 4, 5, 2, 2, 3, 0, 2, 4, 2, 3, 3, 3, 0, 3, 1,
## 1, 4, 1, 4, 2, 5, 1, 0, 2, 2, 3, 1, 1, 1, 2, 3, 2, 0, 0, 2, 1,
## 0, 0, 4, 3, 3, 2, 1, 3, 0, 2, 3, 2, 5, 2, 6, 3, 3, 9, 5, 4, 3,
## 2, 5, 0, 2, 1, 1, 3, 1, 3, 2, 0, 5, 2, 4, 2, 3, 1, 0, 1, 4, 0,
## 4, 2, 2, 2, 3, 2, 2, 0, 1, 4, 1, 5, 2, 2, 7, 2, 2, 0, 2, 4, 3,
## 2, 5, 3, 0, 3, 1, 2, 7, 4, 2, 7, 1, 0, 3, 0, 2, 1, 1, 0, 2, 1,
## 3, 0, 3, 0, 3, 1, 1, 2, 1, 2, 1, 2, 0, 2, 2, 3, 3, 1, 4, 2, 4,
## 2, 2, 2, 0, 3, 0, 1, 2, 3, 2, 0, 4, 3, 3, 4, 2, 2, 0, 0, 3, 2,
## 4, 4, 0, 4, 3, 0, 3, 0, 3, 3, 3, 1, 3, 6, 2, 4, 3, 2, 3, 6, 3,
## 3, 0, 0, 4, 1, 3, 6, 2, 5, 2, 2, 1, 2, 2, 4, 4, 2, 2, 1, 2, 0,
## 0, 0, 2, 1, 0, 3, 1, 0, 5, 2, 4, 0, 2, 1, 3, 1, 2, 0, 3, 3, 5,
## 2, 5, 3, 2, 3, 3, 2, 2, 1, 5, 1, 4, 4, 0, 1, 2, 2, 4, 1, 3, 2,
## 1, 3, 5, 4, 1, 3, 0, 2, 2, 3, 3, 2, 0, 4, 2, 4, 5, 3, 7, 0, 2,
## 1, 0, 3, 3, 2, 2, 1, 3, 1, 1, 5, 2, 0, 2, 1, 3, 1, 4, 1, 2, 3,
## 4, 0, 3, 0, 0, 1, 3, 1, 2, 1, 1, 0, 0, 2, 2, 6, 1, 1, 1, 4, 6,
## 6, 6, 3, 4, 1, 1, 0, 2, 2, 1, 0, 3, 4, 2, 1, 4, 1, 5, 2, 0, 4,
## 5, 3, 2, 3, 4, 0, 3, 1, 6, 2, 5, 3, 5, 7, 9, 0, 4, 4, 1, 4, 1,
## 2, 3, 2, 4, 5, 4, 4, 1, 3, 2, 2, 3, 2, 2, 4, 0, 0, 1, 1, 1, 2,
## 4, 1, 9, 2, 5, 2, 2, 5, 2, 2, 2, 0, 6, 3, 3, 1, 4, 4, 4, 5, 1,
## 3, 4, 0, 3, 4, 1, 1, 3, 0, 4, 4, 1, 3, 1, 4, 1, 2, 3, 3, 3, 0,
## 3, 0, 2, 1, 2, 0, 0, 2, 3, 3, 2, 0, 6, 2, 4, 3, 0, 0, 1, 0, 1,
## 1, 0, 3, 2, 0, 1, 5, 3, 2, 4, 0, 1, 3, 0, 1, 4, 0, 1, 2, 2, 0,
## 4, 2, 4, 2, 2, 1, 4, 4, 0, 1, 1, 1, 2, 3, 2, 2, 6, 4, 4, 2, 1,
## 2, 4, 4, 0, 1, 1, 1, 2, 5, 3, 3, 1, 4, 5, 2, 4, 3, 0, 2, 3, 6,
## 0, 5, 6, 7, 3, 5, 1, 3, 3, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 3, 2,
## 0, 3, 2, 4, 3, 5, 4, 3, 3, 2, 1, 3, 0, 0, 3, 3, 2, 2, 7, 3, 0,
## 1, 0, 4, 4, 2, 2, 5, 1, 1, 0, 2, 2, 4, 3, 0, 3, 6, 3, 4, 3, 0,
## 0, 3, 4, 2, 2, 1, 3, 3, 3, 3, 2, 1, 0, 2, 4, 2, 3, 2, 1, 1, 0,
## 3, 0, 2, 4, 5, 1, 3, 3, 0, 3, 3, 4, 2, 0, 5, 5, 1, 1, 2, 0, 3,
## 5, 0, 0, 4, 2, 2, 6, 4, 0, 2, 1, 3, 0, 0, 3, 3, 2), c(1, 0, 0,
## 3, 9, 2, 0, 2, 1, 1, 3, 2, 1, 4, 1, 2, 2, 2, 5, 0, 0, 0, 6, 0,
## 1, 1, 1, 2, 0, 0, 2, 0, 3, 2, 1, 3, 2, 1, 0, 0, 0, 1, 3, 2, 1,
## 1, 1, 1, 0, 0, 0, 1, 1, 3, 1, 0, 1, 0, 1, 1, 1, 1, 2, 0, 0, 3,
## 1, 7, 2, 0, 3, 3, 1, 4, 2, 0, 1, 5, 6, 1, 1, 0, 6, 1, 0, 2, 3,
## 2, 2, 1, 0, 7, 1, 0, 1, 2, 0, 1, 1, 1, 1, 4, 3, 4, 4, 0, 9, 4,
## 0, 0, 2, 2, 2, 4, 1, 2, 2, 1, 0, 1, 0, 0, 0, 1, 2, 0, 2, 7, 1,
## 1, 2, 1, 0, 5, 3, 1, 2, 0, 3, 6, 1, 3, 0, 0, 1, 0, 0, 7, 3, 4,
## 3, 6, 0, 2, 2, 2, 1, 1, 0, 0, 1, 2, 0, 4, 2, 0, 2, 2, 0, 0, 1,
## 4, 1, 1, 0, 1, 2, 2, 1, 2, 4, 2, 0, 0, 2, 2, 0, 3, 2, 3, 1, 1,
## 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 1, 1, 1, 2, 1, 0, 3,
## 0, 1, 3, 0, 1, 2, 3, 0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 3, 2, 0,
## 0, 3, 0, 0, 0, 2, 3, 3, 0, 1, 0, 3, 5, 0, 2, 2, 1, 3, 1, 1, 1,
## 0, 1, 0, 2, 2, 3, 4, 5, 0, 1, 1, 2, 0, 3, 1, 0, 0, 0, 0, 0, 0,
## 2, 1, 1, 1, 0, 0, 2, 3, 2, 3, 2, 2, 3, 2, 0, 0, 2, 2, 9, 1, 0,
## 4, 0, 0, 0, 3, 1, 3, 3, 3, 1, 0, 4, 0, 2, 0, 1, 7, 3, 5, 1, 2,
## 1, 2, 0, 2, 1, 3, 0, 3, 3, 1, 1, 1, 1, 1, 0, 2, 2, 1, 0, 1, 1,
## 3, 1, 0, 1, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 2, 1, 0, 0, 2, 1,
## 0, 3, 2, 1, 2, 0, 0, 1, 0, 3, 4, 1, 9, 1, 3, 0, 1, 3, 0, 0, 0,
## 1, 0, 2, 3, 1, 3, 1, 1, 2, 0, 0, 0, 2, 5, 2, 1, 3, 1, 0, 0, 2,
## 9, 2, 2, 2, 1, 6, 0, 2, 2, 0, 9, 9, 1, 2, 0, 2, 2, 1, 0, 2, 5,
## 2, 2, 1, 1, 0, 1, 3, 0, 1, 0, 0, 0, 0, 2, 2, 2, 7, 7, 1, 5, 0,
## 3, 1, 0, 2, 0, 1, 3, 3, 0, 3, 4, 1, 2, 0, 1, 3, 3, 4, 2, 1, 1,
## 2, 3, 1, 2, 1, 2, 0, 1, 1, 2, 4, 2, 0, 1, 0, 0, 2, 0, 1, 3, 1,
## 0, 0, 5, 0, 3, 1, 1, 3, 2, 2, 2, 0, 3, 3, 0, 0, 3, 0, 3, 0, 2,
## 2, 0, 3, 2, 2, 2, 3, 3, 2, 0, 0, 1, 1, 0, 0, 3, 1, 0, 1, 7, 1,
## 1, 1, 2, 3, 2, 1, 5, 0, 6, 0, 6, 2, 3, 1, 0, 1, 3, 2, 1, 0, 0,
## 7, 2, 0, 0, 3, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 3, 2, 0, 0, 0, 0,
## 2, 0, 1, 1, 7, 3, 4, 0, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 0, 1, 2,
## 9, 0, 0, 4, 0, 0, 2, 0, 2, 2, 3, 0, 1, 0, 1, 0, 0, 2, 0, 1, 2,
## 0, 2, 1, 3, 0, 0, 0, 2, 1, 1, 0, 2, 2, 2, 3, 1, 0, 0, 2, 2, 2,
## 2, 1, 0, 0, 4, 7, 2, 1, 0, 2, 1, 0, 7, 2, 4, 0, 1, 3, 1, 2, 1,
## 1, 2, 0, 1, 6, 0, 1, 4, 2, 4, 0, 3, 3, 2, 0, 1, 0, 9, 0, 5, 1,
## 1, 1, 0, 3, 1, 3, 0, 2, 1, 5, 2, 0, 1, 2, 0, 1, 3, 2, 2, 0, 7,
## 4, 1, 3, 2, 0, 1, 4, 3, 1, 3, 0, 2, 2, 1, 0, 1, 0, 2, 1, 7, 2,
## 6, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 4, 0, 2, 2, 0, 2, 1, 0, 0, 0,
## 5, 0, 1, 2, 0, 0, 0, 1, 0, 9, 2, 3, 0, 3, 0, 2, 0, 1, 0, 2, 1,
## 0, 0, 2, 3, 2, 0, 2, 1, 5, 0, 1, 1, 1, 3, 1, 2, 1, 0, 4, 4, 2,
## 3, 0, 1, 1, 4, 2, 3, 1, 2, 0, 0, 2, 2, 1, 1, 2, 0, 3, 5, 4, 2,
## 0, 0, 0, 3, 0, 0, 1, 0, 2, 1, 5, 5, 0, 3, 3, 0, 5, 0, 5, 3, 0,
## 2, 2, 0, 4, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 3, 1, 1, 1, 2, 2,
## 0, 4, 1, 5, 0, 1, 1, 1, 2, 1, 0, 2, 1, 3, 0, 2, 1, 0, 2, 2, 1,
## 0, 5, 3, 1, 3, 1, 0, 1, 1, 2, 0, 3, 2, 1, 0, 1, 0, 1, 2, 1, 0,
## 1, 1, 1, 1, 1, 2, 2, 9, 2, 2, 2, 4, 1, 0, 4, 0, 1, 0, 2, 1, 1,
## 0, 0, 2, 6, 1, 0, 2, 1, 0, 3, 1, 0, 4, 5, 1, 2, 0, 0, 0, 1, 1,
## 6, 1, 9, 2, 1, 0, 0, 0, 1, 0, 1, 2, 2, 2, 0, 1, 1, 1, 1, 0, 1,
## 0, 2, 1, 1, 0, 0, 0, 1, 1, 0, 7, 5, 2, 0, 1, 0, 0, 0, 0, 4, 3,
## 0, 2, 1, 3, 0, 0, 0, 0, 0, 2, 0, 3, 4, 1, 1, 9, 2, 0, 1, 1, 1,
## 0, 0, 0, 2, 0, 2, 4, 1, 3, 0), c(1, 2, 5, 2, 0, 2, 1, 1, 1, 2,
## 0, 3, 2, 2, 3, 1, 2, 0, 2, 0, 0, 0, 1, 0, 3, 2, 3, 1, 4, 2, 1,
## 3, 1, 2, 3, 2, 3, 2, 2, 1, 0, 2, 2, 1, 3, 1, 1, 2, 3, 1, 2, 4,
## 1, 0, 2, 4, 1, 3, 1, 2, 2, 2, 1, 5, 3, 2, 1, 0, 1, 1, 0, 2, 1,
## 2, 3, 1, 1, 4, 1, 3, 2, 0, 2, 2, 1, 2, 1, 0, 3, 1, 0, 0, 3, 1,
## 2, 1, 0, 8, 1, 1, 1, 2, 2, 2, 0, 0, 0, 2, 5, 0, 2, 2, 1, 2, 1,
## 2, 1, 2, 6, 0, 2, 0, 0, 3, 5, 0, 3, 2, 4, 3, 3, 1, 1, 0, 2, 2,
## 1, 1, 1, 2, 2, 3, 4, 1, 1, 1, 2, 1, 1, 2, 3, 0, 1, 1, 4, 1, 3,
## 2, 1, 3, 1, 1, 0, 2, 0, 0, 2, 2, 4, 1, 1, 2, 1, 2, 1, 0, 3, 3,
## 0, 1, 2, 1, 0, 0, 1, 1, 3, 1, 2, 2, 1, 2, 0, 1, 0, 0, 3, 0, 1,
## 3, 1, 0, 2, 1, 0, 0, 1, 3, 0, 1, 3, 0, 3, 0, 2, 1, 3, 3, 2, 1,
## 1, 4, 2, 1, 1, 1, 3, 1, 2, 3, 2, 0, 2, 3, 0, 2, 0, 1, 0, 2, 2,
## 3, 0, 1, 4, 3, 3, 0, 1, 2, 1, 2, 1, 1, 0, 3, 1, 1, 2, 2, 0, 4,
## 3, 0, 3, 1, 1, 0, 2, 1, 0, 3, 4, 4, 3, 3, 2, 2, 4, 2, 0, 0, 4,
## 1, 2, 1, 1, 0, 1, 2, 0, 4, 0, 0, 0, 3, 0, 3, 0, 0, 0, 2, 2, 0,
## 2, 2, 0, 0, 0, 2, 0, 1, 3, 0, 1, 2, 0, 2, 1, 2, 3, 2, 2, 2, 0,
## 1, 0, 1, 3, 3, 1, 5, 2, 1, 3, 2, 3, 2, 2, 2, 3, 0, 0, 1, 2, 3,
## 0, 2, 0, 5, 2, 1, 2, 0, 1, 4, 4, 3, 1, 2, 0, 2, 2, 1, 1, 2, 0,
## 2, 0, 1, 3, 1, 0, 1, 3, 4, 2, 2, 0, 1, 0, 0, 0, 1, 3, 1, 2, 2,
## 2, 5, 0, 2, 9, 2, 2, 3, 2, 1, 2, 2, 2, 1, 0, 2, 2, 2, 2, 1, 5,
## 2, 2, 2, 0, 0, 2, 3, 0, 0, 2, 3, 0, 1, 1, 2, 4, 1, 3, 2, 2, 2,
## 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 3, 0, 1, 0, 3, 3, 0, 0, 0,
## 2, 0, 2, 4, 3, 1, 0, 1, 1, 4, 2, 0, 5, 2, 2, 1, 2, 3, 0, 1, 5,
## 2, 1, 1, 0, 3, 0, 1, 0, 1, 2, 2, 2, 4, 1, 0, 0, 3, 0, 1, 0, 1,
## 3, 2, 2, 3, 3, 1, 2, 1, 0, 1, 1, 1, 4, 3, 1, 0, 0, 3, 2, 2, 2,
## 2, 2, 1, 4, 2, 3, 1, 2, 2, 2, 0, 1, 2, 2, 1, 1, 3, 1, 1, 1, 0,
## 1, 0, 0, 0, 3, 0, 1, 4, 1, 5, 2, 1, 0, 9, 0, 2, 6, 4, 1, 0, 0,
## 2, 1, 3, 1, 2, 0, 3, 2, 2, 3, 0, 2, 1, 1, 1, 1, 2, 4, 1, 1, 4,
## 0, 1, 1, 2, 4, 2, 0, 0, 3, 1, 4, 0, 1, 2, 0, 1, 0, 1, 5, 0, 2,
## 2, 2, 5, 1, 0, 2, 0, 5, 0, 1, 2, 3, 0, 2, 2, 1, 1, 2, 1, 0, 4,
## 2, 2, 2, 1, 1, 2, 0, 1, 1, 4, 0, 1, 0, 2, 1, 1, 0, 0, 3, 0, 2,
## 3, 0, 0, 0, 1, 0, 2, 2, 6, 2, 0, 2, 2, 1, 1, 1, 2, 1, 0, 2, 1,
## 3, 1, 1, 0, 1, 2, 0, 2, 1, 2, 0, 1, 2, 2, 3, 1, 4, 3, 2, 1, 2,
## 2, 1, 2, 2, 3, 1, 2, 0, 0, 1, 1, 1, 0, 0, 3, 1, 2, 3, 0, 2, 3,
## 3, 2, 2, 2, 1, 3, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 1, 3, 1, 0,
## 0, 0, 1, 2, 2, 1, 2, 1, 1, 3, 2, 1, 0, 2, 1, 0, 2, 5, 1, 1, 4,
## 2, 4, 0, 2, 2, 3, 1, 1, 2, 0, 2, 3, 2, 2, 1, 0, 1, 2, 0, 2, 2,
## 1, 2, 1, 2, 2, 2, 3, 1, 1, 0, 4, 2, 1, 2, 0, 0, 2, 0, 2, 2, 2,
## 2, 3, 5, 2, 2, 3, 2, 0, 2, 0, 3, 1, 0, 3, 3, 0, 0, 3, 3, 1, 1,
## 2, 1, 1, 2, 0, 3, 3, 2, 3, 0, 4, 2, 1, 0, 2, 2, 0, 1, 2, 2, 1,
## 2, 2, 2, 2, 3, 2, 0, 0, 0, 2, 3, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1,
## 2, 2, 0, 0, 1, 1, 2, 0, 1, 3, 4, 2, 3, 3, 5, 0, 2, 4, 1, 2, 0,
## 1, 2, 1, 4, 2, 4, 2, 6, 4, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 4, 2,
## 0, 1, 2, 3, 2, 1, 5, 4, 2, 2, 0, 2, 1, 2, 0, 2, 1, 1, 3, 6, 2,
## 1, 4, 1, 3, 0, 2, 2, 1, 1, 0, 0, 3, 3, 0, 0, 3, 0, 1, 2, 0, 0,
## 3, 0, 0, 0, 1, 2, 2, 5, 3, 1, 1, 2, 4, 1, 0, 2, 1, 3, 2, 2, 0,
## 0, 2, 2, 0, 2, 4, 2, 2, 1, 4, 0, 3, 2, 2, 4, 2, 3, 2, 3, 4, 0,
## 2, 2, 2, 2, 2, 2, 1, 0, 0, 3, 0, 2, 1, 2, 0, 0, 2, 1, 0, 3, 0,
## 3, 1, 0), c(2, 3, 0, 1, 0, 2, 4, 2, 0, 1, 6, 4, 2, 1, 2, 2, 4,
## 0, 1, 0, 3, 5, 3, 4, 3, 2, 3, 5, 0, 1, 4, 6, 1, 1, 3, 2, 4, 3,
## 4, 1, 5, 4, 2, 3, 2, 1, 2, 2, 2, 1, 0, 1, 1, 2, 1, 0, 1, 2, 4,
## 4, 3, 2, 3, 0, 4, 2, 2, 0, 5, 1, 4, 2, 3, 2, 4, 4, 2, 0, 1, 4,
## 2, 5, 1, 2, 2, 2, 3, 3, 3, 1, 4, 2, 2, 4, 3, 4, 0, 0, 4, 3, 1,
## 4, 2, 0, 2, 0, 0, 1, 0, 0, 3, 2, 2, 4, 3, 1, 2, 0, 0, 0, 1, 0,
## 4, 1, 0, 0, 3, 0, 1, 3, 3, 2, 1, 0, 4, 4, 2, 3, 3, 0, 3, 2, 2,
## 5, 0, 1, 0, 1, 6, 2, 2, 2, 1, 6, 2, 3, 3, 3, 1, 2, 2, 1, 2, 3,
## 2, 2, 3, 3, 0, 3, 3, 0, 4, 1, 5, 2, 2, 3, 1, 3, 2, 3, 4, 6, 2,
## 3, 4, 3, 3, 3, 5, 1, 0, 2, 0, 0, 5, 0, 2, 2, 2, 0, 5, 5, 3, 5,
## 5, 3, 2, 5, 4, 0, 1, 4, 0, 5, 0, 3, 2, 3, 2, 3, 2, 5, 2, 3, 3,
## 3, 2, 3, 2, 3, 2, 0, 0, 3, 0, 2, 2, 3, 3, 1, 6, 5, 0, 0, 2, 0,
## 2, 5, 1, 4, 5, 4, 4, 0, 5, 1, 3, 2, 3, 0, 0, 0, 1, 2, 2, 0, 3,
## 2, 0, 1, 0, 2, 6, 0, 2, 6, 3, 2, 2, 5, 2, 1, 3, 4, 2, 0, 5, 0,
## 4, 3, 2, 5, 0, 3, 2, 2, 2, 5, 3, 3, 1, 2, 3, 0, 0, 0, 4, 2, 2,
## 7, 2, 0, 2, 1, 1, 3, 2, 3, 0, 4, 2, 3, 5, 3, 6, 4, 4, 4, 1, 1,
## 4, 4, 5, 2, 4, 3, 3, 3, 3, 1, 2, 4, 4, 0, 4, 3, 0, 1, 2, 4, 2,
## 2, 2, 2, 0, 1, 1, 4, 4, 2, 3, 2, 3, 3, 3, 5, 5, 3, 2, 3, 0, 5,
## 3, 0, 2, 0, 0, 4, 0, 1, 4, 2, 2, 7, 3, 1, 2, 3, 5, 2, 0, 2, 0,
## 3, 2, 3, 2, 2, 3, 5, 0, 3, 3, 2, 4, 1, 0, 2, 2, 3, 0, 0, 2, 3,
## 5, 0, 3, 2, 1, 1, 2, 1, 2, 2, 2, 0, 4, 2, 2, 3, 1, 2, 3, 0, 4,
## 3, 3, 0, 1, 3, 2, 2, 3, 4, 5, 4, 0, 2, 3, 3, 5, 3, 1, 0, 2, 0,
## 1, 2, 2, 3, 2, 1, 2, 0, 5, 5, 2, 1, 3, 0, 2, 3, 2, 4, 3, 4, 5,
## 1, 1, 1, 4, 3, 1, 2, 2, 3, 1, 2, 5, 4, 5, 2, 2, 3, 2, 1, 2, 3,
## 3, 4, 3, 2, 4, 2, 2, 5, 1, 3, 3, 2, 2, 0, 3, 2, 3, 1, 5, 2, 2,
## 3, 2, 3, 0, 1, 0, 4, 1, 1, 2, 3, 2, 1, 2, 1, 2, 4, 3, 4, 4, 1,
## 3, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2, 3, 1, 2, 2, 2, 1, 2, 4, 0, 2,
## 3, 0, 4, 0, 1, 3, 1, 2, 2, 2, 2, 1, 3, 0, 0, 5, 4, 2, 0, 3, 0,
## 8, 4, 2, 2, 0, 2, 1, 0, 2, 0, 4, 0, 4, 5, 2, 3, 0, 6, 4, 3, 0,
## 2, 2, 3, 1, 0, 4, 3, 5, 3, 1, 5, 1, 0, 0, 4, 2, 3, 1, 3, 4, 1,
## 3, 1, 0, 0, 3, 2, 4, 2, 1, 1, 5, 1, 0, 3, 4, 4, 0, 2, 1, 0, 3,
## 2, 3, 2, 4, 6, 2, 3, 0, 4, 4, 1, 2, 0, 2, 2, 2, 4, 0, 2, 3, 5,
## 0, 1, 3, 0, 1, 2, 2, 3, 1, 1, 1, 4, 3, 3, 3, 0, 1, 3, 2, 3, 1,
## 3, 2, 3, 2, 2, 2, 0, 1, 1, 3, 4, 1, 2, 1, 1, 2, 3, 0, 2, 4, 2,
## 2, 2, 3, 2, 2, 2, 2, 3, 2, 0, 2, 1, 2, 0, 0, 5, 1, 4, 1, 1, 4,
## 5, 3, 0, 2, 1, 0, 0, 2, 0, 3, 0, 1, 5, 3, 2, 0, 0, 2, 2, 1, 3,
## 1, 4, 2, 2, 6, 2, 1, 0, 4, 2, 0, 3, 3, 5, 1, 2, 3, 2, 2, 2, 2,
## 3, 5, 2, 2, 0, 2, 3, 4, 0, 3, 2, 3, 3, 3, 3, 1, 0, 2, 2, 3, 2,
## 2, 0, 0, 1, 2, 4, 4, 4, 0, 5, 2, 4, 2, 4, 4, 4, 5, 3, 4, 0, 1,
## 3, 4, 2, 5, 3, 0, 0, 5, 2, 0, 3, 4, 2, 2, 1, 2, 3, 3, 5, 0, 4,
## 0, 6, 2, 0, 5, 3, 6, 4, 4, 2, 2, 2, 1, 0, 2, 2, 1, 0, 2, 1, 3,
## 4, 5, 2, 0, 0, 1, 3, 0, 0, 2, 3, 2, 2, 0, 1, 2, 1, 0, 3, 1, 1,
## 0, 0, 1, 2, 2, 1, 1, 2, 5, 3, 2, 3, 4, 2, 0, 2, 1, 4, 3, 1, 0,
## 1, 6, 1, 0, 5, 2, 5, 0, 2, 2, 3, 2, 3, 2, 1, 2, 2, 1, 4, 3, 3,
## 0, 1, 0, 0, 0, 0, 0, 2, 3, 0, 2, 2, 0, 1, 1, 4, 0, 2, 2, 1, 0,
## 0, 2, 5, 4, 1, 0, 5, 0, 2, 3, 2, 1, 3, 4, 2, 2, 0, 1, 0, 2, 3,
## 4, 2, 3, 3, 2, 2, 0, 2, 0, 0, 2, 3, 3, 0, 0, 3, 4, 1, 0, 3, 2,
## 1, 0, 4, 0, 1, 3, 1, 0, 0, 3, 6, 1, 2, 4, 2, 2, 2), c(6, 5, 4,
## 4, 0, 4, 5, 5, 8, 4, 0, 1, 5, 4, 4, 5, 2, 7, 2, 7, 6, 4, 1, 5,
## 3, 5, 2, 3, 5, 7, 4, 1, 5, 3, 3, 3, 0, 4, 4, 8, 4, 2, 3, 4, 4,
## 5, 5, 5, 4, 6, 7, 3, 6, 5, 6, 5, 7, 4, 4, 3, 4, 4, 4, 4, 0, 4,
## 6, 2, 2, 4, 2, 2, 5, 2, 1, 3, 5, 0, 1, 3, 3, 4, 2, 5, 6, 3, 3,
## 5, 3, 8, 3, 0, 4, 5, 4, 3, 9, 0, 4, 4, 5, 0, 4, 0, 3, 4, 0, 2,
## 4, 5, 2, 4, 5, 0, 4, 4, 5, 7, 3, 7, 7, 5, 5, 5, 2, 6, 2, 0, 3,
## 4, 2, 3, 5, 4, 0, 3, 5, 5, 3, 2, 4, 2, 4, 3, 5, 7, 7, 2, 0, 2,
## 2, 2, 7, 2, 2, 3, 3, 4, 3, 4, 5, 7, 3, 1, 5, 2, 3, 3, 5, 5, 4,
## 0, 3, 6, 4, 5, 3, 2, 6, 4, 3, 3, 5, 3, 5, 3, 3, 3, 3, 2, 2, 4,
## 7, 5, 9, 9, 2, 9, 5, 4, 5, 5, 2, 2, 5, 4, 2, 3, 7, 2, 2, 6, 3,
## 3, 6, 1, 6, 3, 4, 3, 6, 3, 5, 3, 5, 3, 2, 3, 4, 2, 3, 3, 4, 6,
## 9, 2, 9, 5, 7, 2, 2, 3, 3, 4, 5, 4, 1, 9, 5, 2, 5, 0, 2, 3, 5,
## 6, 4, 5, 3, 4, 4, 2, 2, 9, 5, 6, 4, 5, 2, 6, 5, 5, 3, 2, 0, 6,
## 4, 2, 3, 5, 2, 4, 2, 3, 4, 3, 5, 7, 2, 5, 5, 2, 6, 1, 0, 4, 2,
## 2, 4, 4, 6, 2, 5, 4, 3, 5, 7, 5, 1, 6, 4, 2, 4, 2, 3, 2, 6, 4,
## 5, 4, 6, 3, 5, 2, 4, 3, 0, 4, 3, 2, 6, 3, 3, 3, 0, 4, 3, 4, 4,
## 2, 3, 5, 6, 3, 4, 6, 5, 1, 5, 4, 3, 3, 4, 2, 5, 3, 5, 5, 5, 3,
## 5, 3, 4, 5, 4, 0, 6, 1, 4, 3, 0, 3, 0, 3, 2, 5, 3, 4, 5, 5, 5,
## 6, 5, 5, 2, 1, 2, 6, 4, 1, 3, 3, 0, 4, 3, 2, 5, 3, 5, 6, 3, 2,
## 0, 4, 2, 4, 2, 2, 4, 4, 3, 5, 0, 0, 4, 2, 4, 4, 4, 4, 7, 4, 2,
## 3, 2, 5, 5, 6, 4, 2, 5, 4, 7, 2, 6, 5, 2, 2, 5, 0, 1, 4, 1, 3,
## 3, 5, 2, 0, 9, 5, 3, 2, 4, 3, 2, 3, 5, 9, 6, 4, 1, 2, 4, 3, 5,
## 5, 1, 2, 3, 6, 3, 4, 5, 3, 5, 1, 3, 4, 2, 6, 5, 3, 4, 4, 2, 6,
## 2, 3, 1, 1, 1, 4, 2, 2, 4, 3, 3, 5, 4, 3, 5, 5, 3, 6, 3, 4, 4,
## 2, 8, 3, 2, 4, 5, 4, 2, 3, 6, 5, 2, 4, 5, 3, 3, 5, 9, 7, 0, 3,
## 6, 6, 2, 2, 5, 5, 2, 6, 2, 5, 0, 0, 3, 5, 2, 6, 0, 6, 7, 9, 0,
## 0, 4, 3, 2, 3, 4, 5, 5, 5, 3, 5, 4, 3, 4, 3, 6, 0, 9, 7, 6, 5,
## 5, 6, 5, 3, 1, 3, 2, 5, 2, 5, 4, 5, 4, 7, 1, 0, 5, 4, 9, 4, 5,
## 0, 6, 5, 1, 4, 5, 2, 5, 4, 2, 0, 4, 3, 4, 2, 5, 5, 5, 6, 5, 4,
## 3, 4, 6, 1, 5, 6, 5, 3, 5, 4, 5, 4, 2, 7, 3, 4, 5, 5, 4, 3, 3,
## 5, 6, 3, 4, 2, 2, 4, 2, 3, 7, 4, 7, 2, 2, 2, 0, 5, 3, 2, 4, 5,
## 5, 3, 4, 6, 2, 7, 5, 2, 4, 1, 6, 3, 2, 2, 7, 8, 5, 0, 6, 2, 3,
## 3, 6, 5, 4, 3, 3, 5, 3, 2, 2, 3, 5, 3, 2, 6, 6, 3, 5, 3, 7, 2,
## 2, 7, 3, 0, 7, 5, 2, 4, 5, 2, 7, 5, 0, 6, 6, 4, 5, 4, 4, 0, 3,
## 1, 5, 7, 6, 3, 5, 4, 9, 4, 7, 4, 3, 5, 2, 2, 5, 5, 5, 5, 7, 7,
## 2, 9, 4, 2, 8, 4, 0, 4, 5, 0, 3, 4, 5, 3, 6, 3, 2, 4, 1, 5, 6,
## 4, 5, 5, 4, 5, 3, 2, 5, 1, 5, 5, 5, 5, 2, 6, 2, 2, 3, 0, 2, 3,
## 3, 9, 5, 6, 2, 4, 2, 5, 4, 4, 5, 3, 3, 6, 4, 3, 9, 2, 1, 1, 0,
## 3, 6, 3, 2, 3, 4, 4, 3, 3, 3, 1, 1, 6, 4, 2, 3, 2, 0, 0, 2, 5,
## 2, 3, 7, 3, 4, 3, 6, 5, 5, 5, 3, 2, 6, 5, 7, 0, 5, 4, 1, 3, 2,
## 4, 0, 6, 1, 5, 6, 5, 2, 5, 7, 6, 4, 7, 2, 5, 2, 1, 5, 5, 4, 3,
## 4, 4, 3, 3, 4, 5, 4, 6, 5, 4, 5, 2, 3, 4, 3, 5, 5, 5, 3, 4, 5,
## 5, 2, 4, 4, 4, 0, 5, 0, 5, 6, 0, 1, 5, 4, 2, 2, 5, 9, 2, 6, 3,
## 9, 5, 4, 1, 4, 0, 4, 5, 2, 4, 5, 5, 1, 1, 8, 5, 5, 9, 6, 4, 7,
## 2, 3, 0, 5, 4, 7, 4, 5, 5, 9, 5, 5, 3, 3, 4, 4, 2, 3, 4, 5, 4,
## 6, 4, 3, 2, 5, 5, 5, 4, 5, 7, 1, 3, 2, 5, 4, 6, 3, 3, 4, 2, 5,
## 3, 5, 5, 3, 0, 0, 9, 7, 0, 3, 7, 5, 1, 6, 8, 0, 0, 7, 6, 5, 4,
## 6, 9, 5, 2, 7, 4, 1, 4, 3, 7), c(1, 0, 0, 0, 0, 2, 0, 2, 1, 2,
## 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0,
## 0, 1, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 1, 2, 2, 1, 0, 2, 0, 2,
## 2, 0, 1, 0, 2, 0, 2, 1, 1, 1, 1, 0, 2, 0, 1, 0, 0, 5, 0, 3, 1,
## 0, 0, 2, 3, 0, 3, 0, 3, 0, 0, 2, 0, 2, 0, 0, 0, 0, 3, 0, 1, 0,
## 1, 0, 0, 0, 0, 2, 4, 0, 0, 4, 2, 5, 0, 1, 0, 4, 1, 2, 2, 0, 2,
## 1, 0, 1, 0, 2, 1, 4, 0, 1, 0, 3, 1, 0, 2, 1, 1, 3, 3, 0, 0, 2,
## 1, 1, 0, 0, 1, 1, 0, 0, 3, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0,
## 2, 5, 0, 3, 0, 4, 1, 0, 5, 0, 1, 0, 1, 1, 4, 1, 1, 0, 2, 0, 0,
## 3, 0, 0, 2, 0, 0, 1, 2, 0, 2, 1, 1, 2, 3, 2, 1, 0, 0, 0, 0, 0,
## 0, 1, 3, 0, 0, 0, 1, 2, 1, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 1, 2,
## 0, 0, 2, 1, 2, 1, 0, 3, 2, 1, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1,
## 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 3, 1, 1, 0, 0,
## 0, 0, 1, 2, 2, 4, 1, 1, 4, 1, 3, 2, 0, 0, 2, 0, 0, 1, 5, 1, 1,
## 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 5, 1, 4, 1, 0, 1, 2, 1,
## 1, 0, 2, 4, 0, 0, 2, 1, 1, 0, 1, 0, 3, 0, 1, 0, 0, 0, 2, 0, 0,
## 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 3, 0, 1, 1, 0,
## 0, 0, 4, 0, 1, 0, 0, 5, 1, 1, 0, 1, 2, 2, 0, 1, 0, 1, 1, 5, 0,
## 0, 1, 1, 0, 3, 0, 1, 0, 0, 3, 0, 4, 1, 4, 3, 0, 2, 1, 0, 1, 1,
## 2, 0, 3, 3, 0, 1, 0, 1, 2, 2, 1, 0, 2, 0, 0, 0, 2, 1, 2, 1, 0,
## 1, 2, 1, 0, 0, 1, 1, 0, 3, 0, 0, 2, 2, 1, 2, 0, 2, 0, 2, 1, 2,
## 2, 1, 2, 5, 0, 4, 0, 2, 0, 0, 2, 1, 0, 5, 2, 0, 0, 0, 0, 3, 0,
## 1, 0, 1, 0, 3, 1, 0, 2, 1, 0, 0, 3, 1, 1, 0, 0, 1, 1, 3, 2, 0,
## 1, 3, 1, 0, 0, 2, 0, 3, 3, 2, 0, 1, 0, 1, 5, 4, 0, 7, 0, 1, 0,
## 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0,
## 1, 2, 0, 1, 1, 0, 2, 2, 0, 0, 0, 1, 0, 0, 1, 2, 2, 2, 1, 2, 0,
## 3, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 4, 2,
## 0, 1, 3, 1, 0, 6, 0, 2, 0, 0, 0, 1, 0, 4, 0, 2, 1, 0, 0, 0, 1,
## 4, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 1, 0, 2, 4, 0, 0, 0, 0,
## 2, 1, 0, 0, 2, 1, 5, 0, 2, 1, 0, 0, 0, 0, 0, 1, 2, 0, 3, 3, 0,
## 0, 0, 1, 3, 0, 0, 0, 2, 4, 0, 4, 1, 4, 0, 2, 1, 6, 0, 0, 0, 0,
## 0, 3, 0, 3, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 3, 1, 1, 2, 0, 0, 2,
## 1, 2, 0, 3, 2, 1, 0, 0, 0, 0, 0, 2, 1, 3, 1, 1, 1, 0, 0, 0, 0,
## 1, 6, 0, 1, 0, 3, 5, 0, 2, 1, 1, 2, 1, 0, 0, 1, 1, 0, 2, 1, 0,
## 0, 1, 0, 0, 2, 0, 1, 2, 3, 0, 3, 3, 0, 4, 0, 2, 0, 2, 3, 2, 5,
## 0, 0, 1, 0, 0, 3, 0, 1, 1, 2, 1, 3, 2, 0, 1, 0, 2, 0, 1, 0, 2,
## 3, 0, 0, 2, 0, 1, 1, 3, 0, 5, 1, 0, 1, 1, 5, 0, 2, 0, 0, 3, 0,
## 2, 0, 1, 2, 1, 1, 1, 1, 0, 5, 0, 4, 1, 0, 0, 0, 1, 1, 0, 1, 0,
## 1, 1, 0, 2, 2, 0, 0, 3, 3, 0, 3, 2, 0, 0, 0, 3, 3, 1, 0, 3, 1,
## 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 0, 1, 3, 0,
## 3, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 3, 0, 0, 2, 0, 1, 0, 2, 1, 3,
## 3, 1, 1, 3, 1, 2, 0, 0, 0, 3, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 5,
## 1, 1, 2, 0, 1, 1, 3, 0, 0, 4, 1, 2, 4, 3, 1, 0, 1, 3, 1, 0, 1,
## 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 1, 0, 2, 1, 0, 1, 0, 0,
## 2, 2, 1, 1, 1, 1, 0, 1, 0, 4, 0, 0, 2, 2, 0, 1, 0, 2, 1, 2, 4,
## 1, 0, 0, 2, 1, 2, 3, 0, 1, 2, 1, 3, 0, 0, 3, 1, 3, 3, 3, 0, 0,
## 3, 1, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 1, 4, 2, 0,
## 0, 5, 0, 1, 0, 0, 1, 0, 0, 0, 2, 1, 1, 3, 3, 0, 1, 0, 2, 0, 0,
## 1, 1, 0), c(1, 2, 7, 5, 4, 9, 6, 0, 9, 0, 0, 6, 5, 5, 9, 0, 6,
## 4, 4, 9, 9, 0, 4, 2, 1, 2, 8, 2, 9, 8, 5, 6, 4, 6, 1, 6, 0, 3,
## 7, 3, 9, 1, 4, 6, 0, 5, 5, 8, 5, 4, 9, 7, 9, 1, 1, 2, 8, 0, 7,
## 2, 9, 4, 2, 9, 8, 0, 5, 0, 2, 9, 7, 6, 4, 1, 2, 2, 8, 9, 0, 1,
## 2, 5, 0, 2, 9, 5, 0, 0, 9, 3, 0, 0, 3, 8, 6, 3, 6, 9, 2, 8, 3,
## 0, 0, 0, 2, 9, 4, 6, 7, 9, 1, 9, 0, 8, 0, 8, 2, 8, 0, 4, 6, 9,
## 2, 8, 0, 9, 5, 0, 7, 8, 0, 4, 8, 2, 0, 3, 2, 2, 0, 0, 8, 1, 0,
## 2, 9, 9, 9, 0, 0, 1, 1, 6, 9, 4, 1, 3, 1, 2, 9, 5, 8, 9, 6, 0,
## 4, 8, 2, 2, 5, 8, 8, 0, 1, 1, 4, 1, 9, 0, 8, 2, 0, 5, 3, 5, 2,
## 8, 4, 3, 4, 6, 2, 9, 9, 4, 9, 0, 9, 5, 2, 3, 8, 0, 0, 6, 4, 0,
## 0, 2, 3, 9, 9, 5, 2, 9, 2, 0, 0, 1, 0, 3, 7, 9, 2, 4, 4, 3, 0,
## 7, 4, 5, 3, 4, 5, 9, 2, 0, 5, 6, 1, 1, 3, 6, 0, 8, 2, 0, 0, 9,
## 0, 6, 5, 9, 7, 4, 4, 0, 8, 9, 2, 4, 2, 0, 8, 5, 7, 6, 5, 7, 3,
## 6, 9, 2, 2, 1, 4, 0, 9, 2, 9, 5, 5, 9, 4, 5, 3, 1, 1, 1, 3, 9,
## 2, 2, 9, 6, 4, 8, 5, 1, 9, 0, 9, 3, 8, 3, 3, 7, 4, 9, 0, 7, 4,
## 6, 3, 0, 3, 4, 8, 8, 4, 3, 0, 0, 2, 1, 5, 2, 0, 3, 8, 9, 5, 5,
## 3, 3, 9, 1, 4, 5, 3, 3, 7, 8, 2, 4, 2, 0, 2, 0, 9, 0, 5, 3, 3,
## 8, 7, 4, 0, 7, 2, 5, 2, 3, 3, 4, 2, 5, 4, 0, 0, 2, 3, 7, 4, 3,
## 2, 0, 2, 2, 7, 2, 9, 8, 2, 0, 2, 1, 3, 1, 6, 0, 9, 7, 9, 4, 2,
## 0, 2, 3, 5, 0, 9, 2, 4, 1, 4, 4, 1, 2, 3, 4, 4, 4, 0, 0, 7, 1,
## 9, 3, 9, 3, 9, 7, 1, 6, 0, 5, 4, 0, 8, 4, 6, 4, 9, 5, 3, 9, 5,
## 4, 3, 0, 2, 9, 0, 9, 3, 1, 9, 0, 9, 5, 3, 3, 9, 3, 0, 2, 7, 2,
## 9, 3, 0, 1, 9, 5, 3, 4, 0, 8, 1, 8, 5, 7, 8, 2, 2, 0, 4, 9, 8,
## 9, 9, 6, 2, 4, 8, 6, 8, 0, 1, 7, 0, 2, 8, 5, 3, 2, 1, 7, 3, 3,
## 7, 9, 2, 2, 4, 0, 9, 2, 1, 2, 0, 4, 0, 2, 3, 5, 3, 2, 8, 4, 9,
## 9, 4, 3, 5, 6, 0, 5, 5, 8, 5, 4, 7, 5, 4, 9, 0, 2, 0, 0, 4, 3,
## 2, 5, 9, 9, 6, 2, 0, 0, 3, 3, 7, 3, 9, 6, 0, 7, 1, 4, 5, 9, 7,
## 9, 7, 0, 0, 8, 3, 8, 2, 9, 8, 9, 1, 3, 1, 9, 2, 8, 4, 1, 2, 1,
## 8, 0, 4, 0, 0, 8, 3, 4, 9, 9, 0, 5, 2, 0, 0, 3, 0, 0, 4, 4, 9,
## 2, 9, 2, 2, 0, 1, 1, 4, 2, 8, 0, 8, 5, 2, 2, 8, 2, 8, 2, 5, 4,
## 3, 7, 9, 9, 2, 3, 1, 0, 1, 9, 4, 0, 0, 9, 5, 9, 4, 9, 1, 0, 1,
## 0, 0, 4, 4, 2, 3, 4, 9, 3, 2, 8, 0, 4, 5, 1, 4, 4, 5, 2, 3, 0,
## 9, 3, 7, 6, 4, 0, 2, 2, 5, 2, 1, 2, 0, 9, 1, 8, 2, 4, 0, 7, 1,
## 9, 7, 8, 7, 7, 1, 0, 2, 6, 3, 0, 9, 5, 0, 1, 5, 1, 6, 0, 0, 4,
## 6, 9, 2, 9, 9, 0, 3, 4, 6, 5, 6, 1, 5, 8, 5, 0, 9, 9, 2, 8, 3,
## 1, 7, 7, 5, 9, 5, 9, 1, 5, 8, 0, 9, 4, 0, 6, 5, 4, 6, 0, 2, 4,
## 9, 8, 5, 6, 6, 7, 6, 4, 2, 0, 2, 0, 5, 6, 5, 0, 8, 2, 5, 1, 1,
## 5, 6, 8, 2, 0, 0, 2, 4, 4, 8, 4, 0, 3, 1, 8, 7, 7, 9, 5, 8, 3,
## 9, 9, 3, 2, 6, 0, 0, 4, 7, 9, 1, 2, 3, 3, 9, 8, 0, 0, 1, 7, 1,
## 0, 9, 4, 3, 0, 2, 9, 6, 7, 9, 3, 2, 2, 2, 1, 5, 3, 4, 9, 0, 9,
## 5, 0, 2, 6, 9, 2, 4, 9, 0, 8, 0, 5, 8, 9, 6, 7, 1, 5, 4, 8, 0,
## 2, 6, 0, 5, 8, 5, 1, 9, 6, 6, 9, 2, 5, 9, 5, 5, 6, 7, 3, 2, 0,
## 0, 5, 8, 8, 4, 8, 3, 8, 8, 2, 5, 2, 0, 6, 0, 2, 0, 0, 0, 5, 9,
## 0, 2, 8, 0, 0, 8, 8, 5, 0, 8, 4, 3, 0, 5, 5, 7, 3, 8, 1, 0, 0,
## 9, 5, 9, 0, 2, 6, 4, 6, 2, 0, 0, 7, 5, 9, 7, 1, 9, 1, 7, 6, 3,
## 5, 3, 2, 1, 9, 0, 8, 7, 4, 7, 7, 1, 3, 2, 9, 8, 9, 2, 2, 7, 7,
## 8, 0, 4, 0, 5, 0, 7, 2, 6, 9, 6, 4, 0, 5, 6, 5, 6, 8, 5, 0, 9,
## 5, 6, 0, 5, 6, 1, 0, 5, 0, 4, 0, 9, 3, 0, 3, 3, 3), c(8, 7, 2,
## 4, 5, 0, 3, 9, 0, 9, 9, 3, 4, 4, 0, 9, 3, 5, 5, 0, 0, 9, 5, 7,
## 8, 7, 1, 7, 0, 1, 4, 3, 5, 3, 8, 3, 9, 6, 2, 6, 0, 8, 5, 3, 9,
## 4, 4, 1, 4, 5, 0, 2, 0, 8, 8, 7, 1, 9, 2, 7, 0, 5, 7, 0, 1, 9,
## 4, 9, 7, 0, 2, 3, 5, 8, 7, 7, 1, 0, 9, 8, 7, 5, 9, 7, 0, 4, 9,
## 9, 0, 6, 9, 9, 6, 1, 3, 6, 3, 0, 7, 1, 6, 9, 9, 9, 7, 0, 5, 3,
## 2, 0, 8, 0, 9, 1, 9, 1, 7, 1, 9, 5, 3, 0, 7, 1, 9, 0, 4, 9, 2,
## 1, 9, 5, 1, 7, 9, 6, 7, 7, 9, 9, 1, 8, 9, 7, 0, 0, 0, 9, 9, 8,
## 8, 3, 0, 5, 8, 6, 8, 7, 0, 4, 1, 0, 3, 9, 5, 1, 7, 7, 4, 1, 1,
## 9, 8, 8, 5, 8, 0, 9, 1, 7, 9, 4, 6, 4, 7, 1, 5, 6, 5, 3, 7, 0,
## 0, 5, 0, 9, 0, 4, 7, 6, 1, 9, 9, 3, 5, 9, 9, 7, 6, 0, 0, 4, 7,
## 0, 7, 9, 9, 8, 9, 6, 2, 0, 7, 5, 6, 6, 9, 2, 5, 4, 6, 5, 4, 0,
## 7, 9, 4, 3, 8, 8, 6, 3, 9, 1, 7, 9, 9, 0, 9, 3, 4, 0, 2, 5, 5,
## 9, 1, 0, 7, 5, 7, 9, 1, 4, 2, 3, 4, 2, 6, 3, 0, 7, 7, 8, 5, 9,
## 0, 7, 0, 4, 4, 0, 5, 4, 6, 8, 8, 8, 6, 0, 7, 7, 0, 3, 5, 1, 4,
## 8, 0, 9, 0, 6, 1, 6, 6, 2, 5, 0, 9, 2, 5, 3, 6, 9, 6, 5, 1, 1,
## 5, 6, 9, 9, 7, 8, 5, 7, 9, 6, 1, 0, 4, 4, 6, 6, 0, 8, 5, 4, 6,
## 6, 2, 1, 7, 5, 7, 9, 7, 9, 0, 9, 4, 6, 6, 1, 2, 5, 9, 2, 7, 4,
## 7, 6, 6, 5, 7, 4, 5, 9, 9, 7, 6, 2, 5, 6, 7, 9, 7, 7, 2, 7, 0,
## 1, 7, 9, 7, 8, 6, 8, 3, 9, 0, 2, 0, 5, 7, 9, 7, 6, 4, 9, 0, 7,
## 5, 8, 5, 5, 8, 7, 6, 5, 5, 5, 9, 9, 2, 8, 0, 6, 0, 6, 0, 2, 8,
## 3, 9, 4, 5, 9, 1, 5, 3, 5, 0, 4, 6, 0, 4, 5, 7, 9, 7, 0, 9, 0,
## 6, 8, 0, 9, 0, 4, 6, 6, 0, 6, 9, 7, 2, 7, 0, 6, 9, 8, 0, 4, 6,
## 5, 9, 1, 8, 1, 4, 2, 1, 7, 7, 9, 5, 0, 1, 0, 0, 3, 7, 5, 1, 3,
## 1, 9, 8, 2, 9, 7, 1, 4, 6, 7, 8, 2, 6, 6, 2, 0, 7, 7, 5, 9, 0,
## 7, 8, 7, 9, 5, 9, 7, 6, 4, 6, 7, 1, 5, 0, 0, 5, 6, 4, 3, 9, 4,
## 4, 1, 4, 5, 2, 4, 5, 0, 9, 7, 9, 9, 6, 6, 7, 4, 0, 0, 3, 7, 9,
## 9, 6, 6, 2, 6, 0, 3, 9, 2, 8, 5, 4, 0, 2, 0, 2, 9, 9, 1, 6, 1,
## 7, 0, 1, 0, 8, 6, 8, 0, 7, 1, 5, 8, 7, 8, 1, 9, 5, 9, 9, 1, 6,
## 5, 0, 0, 9, 4, 7, 9, 9, 6, 9, 9, 5, 5, 0, 7, 0, 7, 7, 9, 8, 8,
## 5, 7, 1, 9, 1, 4, 7, 7, 1, 7, 1, 7, 4, 5, 6, 2, 0, 0, 7, 6, 8,
## 9, 8, 0, 5, 9, 9, 0, 4, 0, 5, 0, 8, 9, 8, 9, 9, 5, 6, 7, 6, 5,
## 0, 6, 7, 1, 9, 5, 4, 8, 5, 5, 4, 7, 6, 9, 0, 6, 2, 3, 5, 9, 7,
## 7, 4, 7, 8, 7, 9, 0, 8, 1, 7, 5, 9, 2, 8, 0, 2, 1, 2, 2, 8, 9,
## 7, 3, 6, 9, 0, 4, 9, 8, 4, 8, 3, 9, 9, 5, 3, 0, 7, 0, 0, 9, 6,
## 5, 3, 4, 3, 8, 4, 1, 5, 9, 0, 0, 7, 1, 6, 8, 2, 2, 4, 0, 4, 0,
## 8, 4, 1, 9, 0, 5, 9, 3, 4, 5, 3, 9, 7, 5, 0, 1, 4, 3, 3, 2, 3,
## 5, 7, 9, 7, 9, 4, 3, 4, 9, 1, 7, 4, 8, 8, 4, 3, 1, 7, 9, 9, 7,
## 6, 5, 1, 5, 9, 6, 8, 1, 2, 2, 0, 4, 1, 6, 0, 0, 6, 7, 3, 9, 9,
## 5, 2, 0, 8, 7, 6, 6, 0, 1, 9, 9, 8, 2, 8, 9, 0, 5, 6, 9, 7, 0,
## 3, 2, 0, 6, 7, 7, 7, 8, 4, 6, 5, 0, 9, 0, 4, 9, 7, 3, 0, 7, 5,
## 0, 9, 1, 9, 4, 1, 0, 3, 2, 8, 4, 5, 1, 9, 7, 3, 9, 4, 1, 4, 8,
## 0, 3, 3, 0, 7, 4, 0, 4, 4, 3, 2, 6, 7, 9, 9, 4, 1, 1, 5, 1, 6,
## 1, 1, 7, 4, 7, 9, 3, 9, 7, 9, 9, 9, 4, 0, 9, 7, 1, 9, 9, 1, 1,
## 4, 9, 1, 5, 6, 9, 4, 4, 2, 6, 1, 8, 9, 9, 0, 4, 0, 9, 7, 3, 5,
## 3, 7, 9, 9, 2, 4, 0, 2, 8, 0, 8, 2, 3, 6, 4, 6, 7, 8, 0, 9, 1,
## 2, 5, 2, 2, 8, 6, 7, 0, 1, 0, 7, 7, 2, 2, 1, 9, 5, 9, 4, 9, 2,
## 7, 3, 0, 3, 5, 9, 4, 3, 4, 3, 1, 4, 9, 0, 4, 3, 9, 4, 3, 8, 9,
## 4, 9, 5, 9, 0, 6, 9, 6, 6, 6), c(8, 7, 7, 9, 6, 5, 8, 4, 5, 6,
## 6, 7, 6, 7, 5, 4, 7, 6, 7, 7, 7, 7, 7, 5, 8, 7, 9, 7, 3, 5, 7,
## 7, 5, 6, 8, 7, 7, 6, 3, 6, 6, 7, 6, 6, 6, 5, 6, 5, 5, 5, 7, 6,
## 7, 3, 8, 6, 8, 9, 8, 4, 5, 5, 5, 7, 2, 7, 5, 9, 6, 4, 7, 7, 7,
## 8, 7, 6, 6, 8, 9, 7, 7, 6, 7, 7, 4, 4, 6, 9, 5, 7, 6, 9, 7, 3,
## 7, 6, 9, 8, 5, 7, 6, 6, 7, 4, 7, 5, 6, 7, 7, 6, 8, 5, 4, 6, 7,
## 1, 7, 5, 6, 3, 7, 6, 5, 6, 6, 5, 7, 5, 6, 5, 9, 7, 4, 7, 6, 5,
## 4, 5, 6, 7, 5, 6, 6, 7, 5, 7, 7, 5, 6, 8, 7, 7, 7, 7, 9, 4, 9,
## 7, 7, 5, 6, 6, 6, 6, 7, 4, 6, 4, 6, 7, 6, 4, 8, 8, 8, 5, 5, 7,
## 6, 5, 6, 7, 7, 7, 4, 1, 9, 7, 6, 7, 7, 5, 7, 6, 7, 6, 9, 9, 7,
## 7, 7, 3, 7, 6, 9, 6, 6, 5, 5, 4, 5, 5, 7, 6, 7, 3, 3, 9, 6, 7,
## 7, 3, 7, 4, 5, 4, 9, 6, 4, 7, 6, 5, 6, 3, 9, 6, 4, 5, 6, 8, 6,
## 6, 7, 8, 6, 7, 7, 7, 4, 6, 5, 5, 7, 7, 7, 6, 3, 7, 4, 6, 7, 5,
## 5, 9, 4, 7, 6, 5, 6, 8, 6, 7, 5, 9, 5, 3, 2, 5, 3, 6, 5, 7, 7,
## 4, 6, 6, 8, 5, 7, 5, 5, 6, 5, 4, 6, 5, 5, 7, 3, 6, 7, 6, 6, 5,
## 6, 5, 3, 6, 9, 4, 4, 4, 6, 9, 7, 7, 6, 9, 6, 7, 3, 5, 7, 7, 9,
## 7, 6, 7, 8, 5, 6, 7, 6, 4, 3, 5, 9, 6, 6, 6, 9, 6, 4, 5, 7, 3,
## 5, 5, 6, 9, 7, 6, 9, 4, 6, 4, 6, 6, 4, 4, 5, 6, 6, 6, 5, 6, 5,
## 9, 6, 7, 4, 6, 6, 4, 9, 6, 5, 7, 5, 5, 6, 6, 5, 4, 5, 3, 6, 8,
## 4, 5, 7, 4, 6, 6, 7, 9, 7, 7, 5, 4, 3, 6, 6, 7, 4, 6, 7, 7, 6,
## 6, 6, 5, 3, 7, 5, 7, 2, 6, 7, 8, 1, 7, 7, 6, 7, 6, 8, 9, 5, 5,
## 6, 6, 8, 5, 8, 6, 5, 4, 5, 7, 8, 5, 7, 7, 7, 7, 9, 7, 3, 5, 5,
## 6, 3, 6, 6, 5, 6, 9, 7, 7, 6, 6, 7, 7, 6, 7, 3, 4, 7, 6, 7, 7,
## 5, 5, 4, 9, 9, 7, 8, 1, 7, 6, 9, 6, 4, 8, 4, 6, 6, 2, 3, 6, 8,
## 7, 6, 7, 7, 6, 6, 6, 8, 5, 7, 9, 7, 7, 7, 6, 5, 5, 9, 6, 6, 7,
## 6, 4, 6, 3, 4, 9, 7, 2, 6, 6, 9, 6, 7, 7, 6, 7, 5, 7, 6, 5, 7,
## 7, 9, 5, 6, 7, 9, 6, 6, 5, 5, 7, 6, 9, 6, 3, 9, 6, 5, 7, 7, 6,
## 6, 6, 8, 6, 9, 5, 4, 3, 6, 7, 6, 5, 6, 6, 7, 5, 6, 2, 5, 5, 8,
## 6, 7, 3, 6, 9, 5, 5, 5, 7, 6, 7, 7, 2, 6, 6, 5, 6, 7, 9, 5, 7,
## 9, 5, 6, 6, 9, 7, 5, 8, 3, 5, 8, 6, 7, 7, 7, 5, 6, 3, 4, 5, 6,
## 6, 5, 5, 5, 5, 5, 7, 7, 6, 3, 6, 5, 5, 5, 4, 6, 1, 7, 6, 9, 7,
## 8, 6, 6, 5, 5, 9, 6, 4, 7, 7, 9, 5, 6, 7, 5, 5, 7, 6, 9, 9, 6,
## 7, 5, 7, 5, 7, 6, 6, 7, 7, 7, 9, 5, 8, 7, 5, 6, 3, 7, 7, 6, 6,
## 6, 4, 6, 6, 9, 6, 5, 7, 7, 5, 6, 5, 6, 9, 7, 6, 6, 7, 8, 6, 6,
## 7, 6, 7, 3, 4, 7, 6, 5, 5, 5, 7, 5, 3, 5, 7, 6, 6, 5, 8, 4, 6,
## 7, 9, 7, 7, 6, 5, 6, 7, 8, 6, 5, 7, 8, 7, 7, 7, 6, 6, 7, 7, 6,
## 5, 6, 6, 6, 7, 7, 5, 7, 5, 5, 5, 7, 7, 6, 9, 5, 4, 7, 9, 9, 6,
## 5, 7, 7, 7, 6, 7, 6, 6, 6, 9, 4, 4, 8, 6, 9, 7, 6, 6, 6, 6, 7,
## 6, 7, 7, 8, 4, 4, 5, 5, 7, 7, 6, 4, 9, 7, 9, 7, 7, 7, 9, 5, 7,
## 6, 7, 6, 5, 4, 9, 7, 6, 6, 7, 6, 6, 5, 6, 6, 5, 7, 6, 7, 7, 9,
## 8, 6, 9, 6, 9, 9, 5, 8, 6, 7, 4, 7, 7, 7, 7, 6, 7, 7, 5, 6, 5,
## 5, 7, 5, 5, 6, 8, 6, 5, 6, 6, 6, 5, 7, 9, 7, 7, 7, 3, 5, 6, 6,
## 6, 6, 7, 6, 6, 4, 6, 6, 7, 6, 5, 6, 3, 8, 5, 8, 5, 8, 5, 6, 7,
## 7, 7, 7, 7, 3, 5, 7, 6, 6, 6, 6, 7, 5, 5, 7, 9, 6, 7, 6, 7, 6,
## 5, 5, 7, 6, 5, 6, 5, 5, 7, 6, 6, 5, 4, 3, 7, 5, 7, 4, 5, 8, 7,
## 6, 7, 6, 5, 6, 6, 6, 9, 6, 7, 6, 5, 5, 8, 7, 6, 6, 6, 8, 9, 5,
## 5, 6, 7, 8, 7, 7, 9, 9, 7, 0, 6, 8, 4, 5, 4, 6, 9, 7, 6, 6, 9,
## 3, 6, 7, 5, 6, 5, 5, 8, 9, 7, 8, 6, 4, 6, 5, 7, 5, 3, 8, 7, 9,
## 6, 7, 5), c(0, 1, 0, 0, 2, 3, 0, 4, 2, 1, 2, 1, 1, 2, 1, 4, 2,
## 1, 1, 2, 2, 0, 2, 4, 0, 0, 0, 2, 2, 1, 0, 1, 4, 1, 0, 1, 2, 2,
## 6, 3, 1, 2, 2, 0, 2, 2, 0, 4, 2, 2, 2, 1, 2, 0, 0, 2, 0, 0, 1,
## 0, 0, 2, 4, 0, 0, 2, 2, 0, 3, 3, 2, 1, 0, 0, 2, 0, 1, 1, 0, 2,
## 0, 2, 2, 0, 0, 2, 3, 0, 1, 1, 2, 0, 0, 0, 0, 2, 0, 1, 3, 0, 1,
## 3, 2, 2, 2, 1, 2, 1, 0, 2, 0, 3, 4, 3, 1, 2, 0, 0, 1, 2, 1, 2,
## 4, 1, 0, 0, 1, 4, 1, 0, 0, 1, 1, 2, 3, 1, 4, 1, 3, 2, 1, 3, 1,
## 1, 2, 2, 0, 4, 3, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 2, 1, 2, 0, 1,
## 2, 2, 2, 0, 2, 1, 1, 2, 0, 0, 1, 2, 1, 2, 1, 4, 2, 2, 1, 2, 4,
## 1, 0, 2, 2, 1, 0, 3, 2, 1, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2,
## 2, 1, 2, 3, 1, 3, 2, 1, 2, 3, 3, 0, 2, 2, 0, 2, 0, 2, 1, 0, 0,
## 0, 0, 1, 1, 4, 2, 2, 0, 3, 3, 1, 2, 0, 2, 2, 2, 1, 2, 0, 2, 0,
## 4, 2, 2, 4, 0, 2, 2, 2, 1, 0, 0, 2, 2, 4, 2, 0, 2, 2, 1, 0, 2,
## 1, 0, 1, 1, 0, 2, 2, 0, 2, 2, 1, 1, 0, 1, 2, 3, 3, 0, 0, 0, 2,
## 4, 2, 0, 3, 2, 0, 1, 0, 0, 2, 2, 2, 1, 4, 2, 2, 2, 2, 0, 2, 4,
## 1, 2, 0, 1, 1, 1, 0, 1, 2, 2, 2, 0, 1, 0, 2, 2, 1, 1, 1, 1, 0,
## 1, 3, 1, 2, 0, 2, 2, 2, 0, 1, 4, 1, 1, 2, 4, 4, 2, 0, 2, 2, 0,
## 2, 0, 2, 3, 2, 3, 5, 4, 1, 3, 1, 4, 1, 0, 0, 2, 2, 4, 0, 2, 0,
## 0, 3, 2, 2, 0, 1, 2, 1, 4, 4, 2, 0, 2, 0, 1, 4, 0, 1, 2, 2, 2,
## 0, 0, 2, 1, 4, 0, 3, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 6, 2, 1, 0,
## 3, 1, 1, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 2, 1, 3, 0, 1, 1, 0, 2,
## 2, 2, 2, 1, 0, 2, 0, 2, 2, 0, 2, 2, 1, 2, 2, 1, 2, 3, 2, 0, 0,
## 2, 0, 1, 1, 0, 0, 2, 2, 3, 0, 0, 1, 2, 0, 4, 2, 4, 0, 0, 0, 0,
## 0, 0, 1, 0, 3, 2, 1, 2, 0, 2, 2, 3, 3, 0, 2, 1, 1, 0, 2, 1, 2,
## 1, 0, 2, 0, 2, 2, 0, 3, 0, 3, 0, 1, 3, 2, 2, 2, 3, 0, 0, 0, 2,
## 0, 2, 1, 0, 1, 2, 2, 1, 1, 2, 2, 0, 2, 0, 0, 0, 4, 3, 2, 0, 1,
## 2, 2, 0, 0, 1, 0, 1, 5, 0, 0, 0, 2, 0, 1, 3, 0, 0, 1, 0, 1, 1,
## 0, 0, 2, 1, 1, 3, 1, 0, 0, 1, 0, 4, 2, 1, 0, 0, 0, 1, 0, 2, 0,
## 0, 2, 1, 2, 1, 2, 2, 2, 0, 0, 2, 0, 4, 2, 0, 1, 0, 3, 0, 2, 1,
## 1, 2, 1, 1, 2, 2, 2, 1, 4, 1, 3, 1, 3, 2, 2, 1, 2, 0, 4, 2, 2,
## 2, 1, 2, 2, 4, 2, 2, 4, 2, 0, 2, 3, 0, 1, 1, 1, 1, 0, 0, 0, 2,
## 5, 2, 2, 0, 2, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 2, 3, 0, 2, 3,
## 0, 1, 0, 0, 2, 1, 0, 1, 1, 0, 0, 0, 3, 2, 1, 2, 3, 2, 0, 1, 1,
## 0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 2, 0, 1, 3, 0, 1, 1, 0, 4, 2, 1,
## 2, 0, 4, 0, 0, 5, 2, 2, 1, 0, 2, 0, 1, 0, 1, 0, 2, 2, 3, 0, 1,
## 2, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 2, 2, 0, 2, 1, 0,
## 0, 1, 1, 2, 1, 0, 1, 0, 4, 4, 2, 0, 0, 2, 2, 2, 1, 0, 1, 0, 3,
## 1, 0, 0, 2, 2, 1, 2, 0, 2, 0, 1, 3, 1, 1, 0, 0, 0, 0, 2, 3, 1,
## 0, 2, 1, 3, 0, 0, 2, 0, 1, 0, 0, 0, 1, 1, 3, 0, 3, 4, 5, 0, 0,
## 3, 2, 0, 1, 3, 0, 0, 2, 1, 2, 2, 1, 0, 0, 1, 1, 0, 2, 0, 0, 0,
## 0, 1, 0, 2, 0, 1, 2, 0, 3, 1, 2, 2, 1, 2, 0, 0, 2, 3, 1, 0, 3,
## 4, 0, 3, 2, 0, 2, 0, 0, 2, 1, 2, 1, 1, 2, 1, 1, 0, 2, 2, 3, 1,
## 1, 0, 1, 4, 2, 0, 1, 1, 0, 2, 1, 2, 1, 1, 2, 0, 2, 2, 6, 2, 0,
## 3, 1, 1, 1, 2, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1, 2, 1, 4,
## 2, 1, 2, 1, 4, 2, 2, 2, 1, 2, 4, 1, 0, 0, 2, 2, 1, 2, 0, 1, 1,
## 0, 2, 0, 2, 3, 1, 1, 1, 2, 0, 1, 1, 0, 4, 0, 1, 2, 1, 2, 1, 0,
## 0, 2, 0, 0, 1, 5, 2, 2, 0, 0, 1, 1, 2, 0, 0, 1, 1, 1, 1, 4, 0,
## 1, 0, 2, 0, 1, 0, 1, 3, 1, 2, 3, 0, 0, 0, 2, 1, 0), c(1, 2, 2,
## 0, 1, 3, 1, 2, 3, 2, 1, 2, 3, 0, 3, 2, 0, 2, 2, 0, 0, 2, 1, 0,
## 1, 2, 0, 0, 4, 4, 2, 2, 1, 3, 1, 2, 0, 2, 0, 0, 3, 0, 1, 3, 2,
## 2, 3, 1, 3, 3, 0, 3, 2, 6, 1, 2, 1, 0, 1, 5, 4, 3, 0, 2, 7, 0,
## 3, 0, 0, 3, 0, 1, 2, 1, 0, 3, 3, 1, 0, 0, 2, 1, 1, 2, 5, 4, 0,
## 0, 3, 1, 2, 0, 2, 6, 2, 1, 0, 1, 2, 2, 2, 0, 0, 4, 0, 3, 1, 1,
## 2, 2, 1, 3, 2, 0, 2, 6, 2, 4, 2, 4, 2, 2, 0, 2, 3, 4, 1, 0, 3,
## 4, 0, 2, 5, 0, 0, 3, 2, 3, 0, 0, 4, 1, 2, 2, 3, 0, 2, 0, 0, 1,
## 2, 0, 2, 0, 0, 5, 0, 2, 2, 3, 3, 2, 3, 2, 0, 4, 1, 5, 2, 1, 2,
## 4, 1, 1, 0, 2, 4, 0, 2, 0, 2, 0, 1, 0, 2, 8, 0, 1, 1, 2, 2, 2,
## 0, 2, 2, 3, 0, 0, 2, 2, 2, 4, 0, 3, 0, 2, 2, 4, 3, 3, 3, 3, 0,
## 3, 0, 3, 4, 0, 2, 1, 2, 4, 2, 4, 4, 5, 0, 3, 5, 1, 3, 0, 1, 4,
## 0, 2, 3, 3, 2, 1, 2, 2, 0, 1, 2, 2, 1, 2, 2, 1, 2, 0, 2, 0, 1,
## 2, 6, 2, 5, 2, 0, 0, 2, 0, 3, 1, 3, 4, 2, 1, 3, 1, 3, 0, 4, 4,
## 7, 2, 4, 3, 3, 2, 2, 4, 0, 0, 1, 4, 2, 3, 0, 1, 4, 3, 1, 4, 3,
## 2, 6, 2, 0, 2, 2, 1, 1, 2, 4, 2, 0, 3, 2, 5, 2, 0, 2, 2, 2, 0,
## 2, 0, 4, 3, 2, 1, 0, 1, 1, 2, 0, 3, 2, 2, 2, 2, 5, 2, 0, 2, 2,
## 2, 0, 3, 2, 3, 2, 4, 0, 0, 2, 0, 0, 1, 0, 4, 3, 3, 0, 1, 2, 1,
## 0, 3, 0, 2, 0, 2, 4, 0, 2, 1, 2, 3, 1, 5, 0, 0, 2, 0, 4, 4, 2,
## 2, 0, 2, 2, 6, 2, 1, 5, 0, 2, 4, 1, 2, 0, 0, 2, 1, 3, 1, 6, 0,
## 1, 0, 3, 2, 0, 1, 1, 3, 2, 3, 0, 0, 3, 2, 5, 3, 2, 0, 8, 1, 2,
## 3, 2, 3, 1, 0, 4, 3, 2, 1, 1, 3, 0, 3, 4, 3, 2, 0, 0, 4, 1, 2,
## 1, 0, 0, 0, 4, 3, 3, 2, 5, 1, 0, 2, 3, 0, 2, 2, 3, 2, 2, 2, 2,
## 0, 3, 5, 2, 2, 0, 2, 1, 2, 2, 0, 0, 2, 1, 8, 2, 3, 0, 1, 4, 1,
## 4, 3, 1, 6, 3, 0, 1, 0, 2, 1, 2, 1, 3, 1, 1, 4, 1, 0, 0, 0, 2,
## 0, 4, 1, 0, 3, 0, 0, 2, 4, 0, 6, 5, 0, 0, 7, 1, 2, 0, 2, 0, 0,
## 2, 2, 3, 0, 3, 2, 2, 2, 0, 0, 0, 0, 0, 2, 1, 3, 4, 2, 2, 0, 3,
## 2, 0, 3, 4, 1, 2, 2, 0, 3, 1, 2, 0, 3, 4, 6, 3, 0, 3, 4, 0, 3,
## 2, 4, 2, 7, 1, 2, 1, 3, 2, 6, 3, 0, 3, 4, 4, 0, 2, 0, 2, 5, 2,
## 1, 4, 3, 1, 0, 0, 0, 0, 3, 3, 0, 0, 0, 3, 0, 4, 3, 0, 2, 0, 0,
## 2, 0, 3, 3, 5, 3, 2, 2, 4, 3, 4, 0, 4, 0, 1, 2, 4, 2, 0, 3, 3,
## 2, 2, 8, 0, 0, 0, 2, 1, 3, 2, 4, 4, 0, 2, 0, 0, 0, 0, 2, 2, 2,
## 3, 4, 2, 3, 0, 0, 3, 2, 4, 1, 3, 2, 2, 0, 2, 1, 2, 0, 3, 0, 2,
## 4, 2, 6, 2, 2, 0, 1, 3, 4, 1, 1, 0, 3, 3, 2, 2, 4, 3, 4, 2, 0,
## 2, 2, 1, 0, 1, 3, 0, 2, 3, 1, 6, 2, 0, 2, 3, 4, 0, 2, 4, 2, 3,
## 1, 2, 3, 3, 1, 5, 3, 2, 0, 0, 1, 1, 4, 3, 0, 1, 3, 3, 2, 1, 2,
## 2, 1, 3, 3, 2, 1, 2, 4, 2, 1, 3, 0, 1, 4, 2, 4, 3, 3, 2, 2, 3,
## 0, 0, 2, 0, 0, 0, 1, 2, 0, 1, 2, 3, 2, 1, 2, 3, 0, 3, 4, 0, 1,
## 0, 0, 3, 2, 0, 3, 1, 3, 2, 2, 1, 4, 3, 4, 4, 1, 2, 0, 5, 0, 0,
## 0, 2, 2, 2, 0, 3, 2, 0, 2, 0, 0, 1, 0, 2, 2, 1, 2, 2, 0, 4, 3,
## 1, 3, 0, 1, 2, 2, 0, 1, 3, 0, 1, 0, 0, 4, 1, 3, 2, 4, 2, 1, 0,
## 2, 0, 2, 0, 2, 2, 3, 4, 2, 2, 3, 2, 1, 2, 0, 3, 0, 2, 4, 0, 0,
## 2, 0, 2, 4, 3, 3, 2, 2, 3, 2, 1, 2, 3, 2, 2, 2, 3, 1, 2, 6, 0,
## 3, 1, 3, 0, 3, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 3, 0, 4, 4,
## 1, 0, 3, 1, 2, 0, 1, 2, 4, 2, 2, 2, 2, 0, 3, 1, 2, 3, 0, 4, 4,
## 0, 4, 0, 2, 3, 1, 2, 1, 0, 2, 2, 3, 3, 2, 0, 2, 2, 2, 2, 3, 1,
## 2, 2, 3, 2, 1, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 9, 3, 0, 0, 2,
## 3, 3, 0, 2, 2, 2, 0, 6, 2, 2, 4, 3, 0, 4, 1, 0, 0, 1, 3, 5, 2,
## 3, 2, 3, 3, 1, 2, 0, 2, 2, 4), c(8, 6, 9, 7, 5, 9, 9, 6, 7, 6,
## 5, 4, 7, 8, 5, 6, 4, 7, 5, 9, 9, 9, 5, 9, 4, 7, 5, 7, 7, 8, 9,
## 6, 7, 8, 4, 6, 7, 6, 6, 9, 7, 7, 4, 7, 5, 7, 6, 8, 6, 8, 9, 8,
## 8, 7, 8, 6, 9, 5, 7, 7, 5, 7, 5, 9, 7, 6, 6, 4, 3, 9, 6, 5, 5,
## 6, 5, 8, 6, 4, 4, 8, 7, 5, 1, 7, 8, 7, 3, 7, 5, 8, 8, 4, 7, 9,
## 7, 5, 9, 4, 5, 6, 7, 3, 6, 5, 5, 8, 5, 2, 9, 7, 6, 9, 6, 0, 6,
## 8, 8, 9, 7, 7, 7, 7, 9, 9, 9, 9, 5, 3, 8, 8, 4, 6, 8, 6, 6, 7,
## 7, 7, 3, 2, 5, 5, 5, 6, 7, 9, 9, 2, 9, 6, 5, 3, 7, 6, 5, 7, 5,
## 7, 9, 6, 6, 7, 9, 6, 5, 7, 5, 7, 8, 9, 8, 5, 5, 8, 9, 7, 4, 2,
## 8, 6, 5, 5, 5, 7, 7, 6, 7, 5, 5, 6, 7, 7, 9, 7, 9, 7, 9, 5, 8,
## 6, 7, 7, 2, 6, 7, 8, 6, 7, 8, 7, 5, 9, 6, 7, 2, 2, 9, 5, 5, 5,
## 7, 6, 7, 7, 8, 7, 3, 8, 7, 5, 7, 4, 2, 7, 7, 5, 9, 8, 8, 6, 6,
## 3, 7, 4, 6, 4, 5, 9, 6, 5, 7, 2, 4, 7, 9, 6, 8, 9, 7, 7, 6, 0,
## 3, 9, 6, 9, 7, 9, 6, 7, 7, 6, 7, 5, 4, 7, 7, 8, 6, 7, 7, 5, 5,
## 4, 5, 5, 7, 2, 8, 7, 9, 5, 9, 4, 5, 8, 7, 5, 7, 8, 9, 6, 8, 6,
## 5, 5, 7, 7, 2, 5, 3, 4, 6, 4, 5, 5, 8, 6, 7, 6, 7, 6, 7, 4, 9,
## 5, 5, 7, 6, 5, 7, 7, 6, 6, 3, 8, 7, 8, 6, 6, 5, 7, 8, 7, 6, 7,
## 9, 0, 7, 5, 4, 5, 0, 7, 7, 7, 2, 5, 7, 7, 9, 7, 5, 7, 5, 8, 9,
## 4, 8, 5, 5, 8, 5, 7, 5, 2, 5, 2, 9, 7, 7, 8, 9, 6, 4, 6, 6, 8,
## 7, 2, 6, 8, 5, 7, 2, 4, 7, 5, 8, 9, 9, 5, 5, 7, 6, 7, 7, 2, 5,
## 6, 6, 7, 3, 2, 6, 5, 3, 6, 6, 6, 8, 5, 4, 8, 6, 6, 8, 9, 8, 6,
## 8, 7, 7, 7, 9, 7, 5, 6, 7, 2, 4, 5, 5, 9, 5, 7, 9, 7, 7, 7, 7,
## 6, 6, 5, 5, 8, 7, 7, 8, 5, 5, 5, 9, 7, 7, 7, 2, 8, 5, 8, 5, 9,
## 8, 5, 7, 2, 3, 9, 7, 8, 9, 8, 9, 7, 8, 7, 7, 9, 5, 7, 2, 7, 7,
## 2, 6, 5, 5, 5, 6, 5, 9, 6, 5, 9, 5, 7, 6, 3, 9, 3, 4, 6, 3, 2,
## 6, 7, 9, 9, 8, 5, 9, 9, 4, 8, 9, 9, 2, 7, 7, 8, 5, 5, 7, 7, 7,
## 7, 2, 9, 2, 7, 6, 7, 5, 6, 2, 4, 9, 9, 2, 2, 5, 8, 7, 5, 6, 8,
## 7, 7, 6, 7, 6, 8, 9, 7, 7, 7, 7, 8, 9, 7, 8, 9, 8, 5, 2, 3, 7,
## 7, 7, 9, 6, 4, 5, 2, 6, 7, 7, 7, 7, 5, 5, 5, 9, 7, 5, 4, 9, 2,
## 9, 7, 9, 9, 9, 1, 8, 3, 9, 7, 7, 6, 7, 7, 6, 5, 9, 2, 8, 9, 6,
## 5, 8, 5, 7, 6, 5, 7, 5, 8, 7, 7, 5, 7, 3, 6, 4, 6, 9, 2, 4, 6,
## 5, 7, 7, 5, 9, 4, 6, 3, 2, 9, 6, 8, 6, 5, 7, 5, 6, 9, 2, 9, 6,
## 5, 7, 6, 9, 5, 6, 3, 9, 8, 9, 2, 8, 3, 7, 7, 7, 9, 8, 3, 3, 6,
## 7, 8, 4, 5, 6, 8, 7, 9, 9, 3, 7, 7, 8, 4, 5, 7, 5, 7, 7, 7, 2,
## 8, 7, 4, 7, 6, 7, 9, 8, 5, 9, 9, 5, 2, 7, 5, 8, 7, 8, 6, 7, 9,
## 6, 5, 9, 8, 4, 7, 5, 7, 9, 9, 8, 9, 8, 9, 4, 8, 4, 9, 7, 7, 6,
## 7, 8, 5, 6, 6, 6, 5, 7, 7, 7, 7, 6, 9, 7, 4, 9, 6, 2, 7, 5, 5,
## 7, 2, 9, 7, 7, 7, 5, 7, 8, 7, 5, 5, 4, 5, 6, 7, 8, 9, 3, 7, 4,
## 8, 7, 9, 7, 7, 7, 6, 5, 5, 7, 2, 4, 2, 7, 7, 7, 6, 5, 9, 6, 7,
## 9, 6, 5, 0, 1, 9, 8, 5, 5, 7, 6, 4, 9, 9, 5, 9, 9, 3, 6, 7, 9,
## 8, 7, 9, 5, 9, 9, 6, 8, 7, 7, 8, 9, 5, 6, 9, 3, 8, 2, 7, 9, 7,
## 6, 9, 7, 9, 7, 9, 5, 9, 8, 4, 8, 9, 7, 5, 9, 3, 6, 6, 5, 7, 7,
## 7, 7, 6, 5, 6, 3, 6, 7, 6, 7, 8, 6, 8, 7, 6, 7, 5, 8, 5, 6, 7,
## 2, 8, 4, 7, 2, 7, 9, 5, 6, 8, 7, 2, 8, 8, 8, 9, 6, 5, 6, 2, 2,
## 7, 7, 5, 9, 7, 6, 0, 7, 8, 7, 7, 5, 8, 7, 3, 7, 2, 6, 6, 8, 6,
## 5, 7, 6, 7, 7, 8, 5, 4, 6, 7, 6, 7, 5, 4, 7, 7, 8, 6, 8, 9, 9,
## 5, 8, 9, 4, 2, 7, 9, 6, 7, 9, 9, 9, 3, 5, 5, 7, 6, 6, 6, 6, 9,
## 7, 8, 5, 8, 6, 0, 8, 4, 2, 7, 8, 7, 6, 6, 9, 7, 7, 2, 7, 6, 2,
## 6, 5, 9), c(1, 3, 0, 2, 4, 0, 0, 3, 2, 3, 4, 5, 2, 1, 4, 3, 5,
## 2, 4, 0, 0, 0, 4, 0, 5, 2, 4, 2, 2, 1, 0, 3, 2, 1, 5, 3, 2, 3,
## 3, 0, 2, 2, 5, 2, 4, 2, 3, 1, 3, 1, 0, 1, 1, 2, 1, 3, 0, 4, 2,
## 2, 4, 2, 4, 0, 2, 3, 3, 5, 6, 0, 3, 4, 4, 3, 4, 1, 3, 5, 5, 1,
## 2, 4, 8, 2, 1, 2, 6, 2, 4, 1, 1, 5, 2, 0, 2, 4, 0, 5, 4, 3, 2,
## 6, 3, 4, 4, 1, 4, 7, 0, 2, 3, 0, 3, 9, 3, 1, 1, 0, 2, 2, 2, 2,
## 0, 0, 0, 0, 4, 6, 1, 1, 5, 3, 1, 3, 3, 2, 2, 2, 6, 7, 4, 4, 4,
## 3, 2, 0, 0, 7, 0, 3, 4, 6, 2, 3, 4, 2, 4, 2, 0, 3, 3, 2, 0, 3,
## 4, 2, 4, 2, 1, 0, 1, 4, 4, 1, 0, 2, 5, 7, 1, 3, 4, 4, 4, 2, 2,
## 3, 2, 4, 4, 3, 2, 2, 0, 2, 0, 2, 0, 4, 1, 3, 2, 2, 7, 3, 2, 1,
## 3, 2, 1, 2, 4, 0, 3, 2, 7, 7, 0, 4, 4, 4, 2, 3, 2, 2, 1, 2, 6,
## 1, 2, 4, 2, 5, 7, 2, 2, 4, 0, 1, 1, 3, 3, 6, 2, 5, 3, 5, 4, 0,
## 3, 4, 2, 7, 5, 2, 0, 3, 1, 0, 2, 2, 3, 9, 6, 0, 3, 0, 2, 0, 3,
## 2, 2, 3, 2, 4, 5, 2, 2, 1, 3, 2, 2, 4, 4, 5, 4, 4, 2, 7, 1, 2,
## 0, 4, 0, 5, 4, 1, 2, 4, 2, 1, 0, 3, 1, 4, 4, 4, 2, 2, 7, 4, 6,
## 5, 3, 5, 4, 4, 1, 3, 2, 3, 2, 3, 2, 5, 0, 4, 4, 2, 3, 4, 2, 2,
## 3, 3, 6, 1, 2, 1, 3, 3, 4, 2, 1, 2, 3, 2, 0, 9, 2, 4, 5, 4, 9,
## 2, 2, 2, 7, 4, 2, 2, 0, 2, 4, 2, 4, 1, 0, 5, 1, 4, 4, 1, 4, 2,
## 4, 7, 4, 7, 0, 2, 2, 1, 0, 3, 5, 3, 3, 1, 2, 7, 3, 1, 4, 2, 7,
## 5, 2, 4, 1, 0, 0, 4, 4, 2, 3, 2, 2, 7, 4, 3, 3, 2, 6, 7, 3, 4,
## 6, 3, 3, 3, 1, 4, 5, 1, 3, 3, 1, 0, 1, 3, 1, 2, 2, 2, 0, 2, 4,
## 3, 2, 7, 5, 4, 4, 0, 4, 2, 0, 2, 2, 2, 2, 3, 3, 4, 4, 1, 2, 2,
## 1, 4, 4, 4, 0, 2, 2, 2, 7, 1, 4, 1, 4, 0, 1, 4, 2, 7, 6, 0, 2,
## 1, 0, 1, 0, 2, 1, 2, 2, 0, 4, 2, 7, 2, 2, 7, 3, 4, 4, 4, 3, 4,
## 0, 3, 4, 0, 4, 2, 3, 6, 0, 6, 5, 3, 6, 7, 3, 2, 0, 0, 1, 4, 0,
## 0, 5, 1, 0, 0, 7, 2, 2, 1, 4, 4, 2, 2, 2, 2, 7, 0, 7, 2, 4, 2,
## 4, 3, 7, 5, 0, 0, 7, 7, 4, 1, 2, 4, 3, 1, 2, 2, 3, 2, 3, 1, 0,
## 2, 2, 2, 2, 1, 0, 2, 1, 0, 1, 4, 7, 6, 2, 2, 2, 0, 3, 5, 4, 7,
## 3, 2, 2, 2, 2, 4, 4, 4, 0, 2, 4, 5, 0, 7, 0, 2, 0, 0, 0, 8, 1,
## 6, 0, 2, 2, 3, 2, 2, 3, 4, 0, 7, 1, 0, 3, 4, 1, 4, 2, 3, 4, 2,
## 4, 1, 2, 2, 4, 2, 6, 3, 5, 3, 0, 7, 5, 3, 4, 2, 2, 4, 0, 5, 3,
## 6, 7, 0, 4, 1, 3, 4, 2, 4, 3, 0, 7, 0, 3, 4, 2, 3, 0, 4, 3, 6,
## 0, 1, 0, 7, 1, 6, 2, 2, 2, 0, 1, 6, 6, 3, 2, 1, 5, 4, 3, 1, 2,
## 0, 0, 6, 2, 2, 1, 5, 4, 2, 4, 2, 2, 2, 7, 1, 2, 5, 2, 3, 2, 0,
## 1, 4, 0, 0, 4, 7, 2, 4, 1, 2, 1, 3, 2, 0, 3, 4, 0, 1, 5, 2, 4,
## 2, 0, 0, 1, 0, 1, 0, 5, 1, 5, 0, 2, 2, 3, 2, 1, 4, 3, 3, 3, 4,
## 2, 2, 2, 2, 3, 0, 2, 5, 0, 3, 7, 2, 4, 4, 2, 7, 0, 2, 2, 2, 4,
## 2, 1, 2, 4, 4, 5, 4, 4, 2, 1, 0, 6, 2, 5, 1, 2, 0, 2, 2, 2, 3,
## 4, 4, 2, 7, 5, 7, 2, 2, 2, 3, 4, 0, 3, 2, 0, 3, 4, 9, 8, 0, 1,
## 4, 4, 2, 3, 5, 0, 0, 4, 0, 0, 6, 3, 2, 0, 1, 2, 0, 4, 0, 0, 3,
## 1, 2, 2, 1, 0, 4, 3, 0, 6, 1, 7, 2, 0, 2, 3, 0, 2, 0, 2, 0, 4,
## 0, 1, 5, 1, 0, 2, 4, 0, 6, 3, 3, 4, 2, 2, 2, 2, 3, 4, 3, 6, 3,
## 2, 3, 2, 1, 3, 1, 2, 3, 2, 4, 1, 4, 3, 2, 7, 1, 5, 2, 7, 2, 0,
## 4, 3, 1, 2, 7, 1, 1, 1, 0, 3, 4, 3, 7, 7, 2, 2, 4, 0, 2, 3, 9,
## 2, 1, 2, 2, 4, 1, 2, 6, 2, 7, 3, 3, 1, 3, 4, 2, 3, 2, 2, 1, 4,
## 5, 3, 2, 3, 2, 4, 5, 2, 2, 1, 3, 1, 0, 0, 4, 1, 0, 5, 7, 2, 0,
## 3, 2, 0, 0, 0, 6, 4, 4, 2, 3, 3, 3, 3, 0, 2, 1, 4, 1, 3, 9, 1,
## 5, 7, 2, 1, 2, 3, 3, 0, 2, 2, 7, 2, 3, 7, 3, 4, 0), c(0, 2, 4,
## 1, 0, 5, 4, 2, 7, 2, 0, 3, 3, 3, 4, 2, 0, 0, 2, 5, 3, 3, 1, 0,
## 0, 0, 2, 4, 9, 5, 5, 4, 4, 4, 0, 3, 0, 2, 7, 3, 4, 2, 2, 4, 0,
## 4, 3, 5, 2, 3, 6, 5, 3, 4, 0, 0, 3, 2, 5, 2, 5, 3, 0, 4, 6, 0,
## 2, 0, 0, 1, 4, 4, 2, 0, 1, 2, 4, 0, 3, 1, 0, 5, 1, 0, 4, 3, 3,
## 0, 4, 0, 0, 0, 0, 2, 1, 0, 3, 0, 2, 5, 3, 0, 0, 3, 2, 5, 0, 2,
## 4, 0, 1, 5, 2, 0, 0, 7, 2, 0, 0, 6, 5, 0, 0, 1, 0, 6, 3, 0, 5,
## 6, 1, 3, 5, 5, 0, 3, 3, 3, 3, 0, 3, 2, 0, 4, 1, 3, 2, 0, 1, 0,
## 1, 2, 6, 4, 2, 2, 3, 1, 8, 2, 4, 2, 3, 0, 2, 7, 2, 4, 0, 2, 3,
## 3, 2, 0, 2, 0, 1, 0, 4, 3, 0, 2, 2, 0, 3, 5, 0, 3, 3, 1, 1, 0,
## 5, 3, 3, 3, 4, 0, 2, 2, 2, 5, 0, 3, 0, 0, 2, 5, 8, 2, 3, 4, 2,
## 3, 0, 2, 4, 3, 0, 3, 1, 3, 0, 6, 4, 2, 2, 5, 5, 3, 3, 0, 2, 9,
## 0, 1, 0, 5, 4, 1, 2, 2, 6, 2, 0, 0, 0, 3, 2, 7, 4, 0, 4, 4, 1,
## 3, 6, 6, 4, 1, 5, 0, 1, 5, 5, 1, 3, 6, 2, 2, 0, 2, 2, 3, 2, 6,
## 6, 4, 3, 3, 0, 4, 4, 3, 0, 4, 2, 4, 2, 3, 0, 3, 6, 3, 0, 6, 0,
## 1, 7, 0, 3, 2, 3, 1, 3, 2, 6, 0, 2, 2, 3, 8, 2, 0, 3, 2, 4, 2,
## 3, 2, 6, 2, 0, 1, 5, 2, 0, 5, 3, 3, 2, 4, 0, 1, 5, 2, 0, 4, 2,
## 2, 2, 7, 5, 2, 2, 6, 0, 0, 0, 3, 3, 0, 0, 7, 4, 2, 0, 5, 3, 2,
## 0, 3, 0, 3, 0, 6, 7, 2, 0, 2, 4, 5, 0, 3, 2, 0, 1, 0, 6, 1, 0,
## 4, 0, 2, 1, 2, 2, 0, 4, 0, 6, 2, 5, 1, 0, 1, 0, 3, 5, 2, 7, 5,
## 0, 1, 2, 1, 2, 2, 0, 4, 3, 5, 0, 0, 5, 1, 3, 0, 5, 5, 7, 3, 2,
## 4, 1, 3, 2, 2, 6, 3, 2, 2, 5, 0, 0, 0, 0, 2, 1, 0, 1, 3, 0, 2,
## 3, 4, 4, 0, 9, 4, 4, 2, 9, 3, 0, 2, 4, 0, 3, 3, 0, 2, 4, 4, 4,
## 0, 2, 7, 1, 4, 2, 4, 5, 3, 3, 2, 0, 4, 2, 8, 6, 4, 0, 2, 2, 2,
## 7, 6, 4, 7, 2, 3, 2, 0, 3, 1, 1, 5, 3, 3, 2, 5, 2, 5, 2, 0, 2,
## 0, 1, 4, 1, 4, 0, 0, 2, 3, 2, 8, 7, 1, 2, 4, 2, 2, 5, 1, 0, 2,
## 2, 3, 3, 3, 4, 4, 0, 7, 0, 0, 0, 0, 3, 3, 3, 2, 2, 0, 1, 3, 0,
## 0, 2, 3, 5, 3, 4, 2, 5, 4, 1, 3, 2, 5, 3, 2, 4, 0, 3, 5, 2, 3,
## 2, 4, 6, 4, 1, 1, 2, 0, 1, 2, 4, 1, 2, 4, 8, 0, 3, 0, 0, 7, 3,
## 0, 4, 1, 0, 0, 0, 0, 1, 3, 0, 1, 2, 1, 5, 1, 6, 3, 0, 3, 4, 1,
## 0, 0, 2, 1, 5, 4, 0, 5, 6, 2, 6, 3, 0, 4, 3, 4, 9, 0, 0, 5, 3,
## 2, 4, 8, 0, 0, 0, 5, 2, 3, 0, 6, 4, 0, 1, 0, 3, 4, 3, 4, 3, 2,
## 1, 1, 2, 2, 0, 5, 3, 1, 5, 3, 4, 2, 2, 3, 2, 0, 3, 0, 3, 0, 0,
## 5, 2, 8, 1, 1, 3, 3, 1, 2, 1, 3, 2, 2, 5, 3, 5, 5, 4, 6, 4, 0,
## 1, 6, 3, 0, 5, 3, 0, 1, 3, 1, 7, 2, 0, 1, 8, 6, 1, 4, 5, 0, 5,
## 1, 2, 3, 8, 1, 6, 2, 0, 2, 3, 4, 1, 6, 1, 1, 2, 5, 5, 6, 2, 2,
## 2, 1, 5, 0, 5, 4, 0, 6, 0, 0, 3, 0, 2, 5, 7, 4, 0, 3, 4, 2, 4,
## 1, 0, 2, 0, 0, 2, 7, 4, 0, 2, 0, 3, 0, 2, 1, 9, 5, 3, 3, 1, 2,
## 3, 0, 6, 1, 1, 3, 1, 6, 3, 4, 4, 3, 3, 4, 6, 6, 0, 2, 4, 2, 0,
## 0, 7, 6, 1, 0, 5, 5, 2, 5, 0, 0, 2, 3, 1, 1, 6, 0, 0, 0, 0, 1,
## 7, 6, 5, 3, 2, 0, 5, 3, 3, 6, 3, 4, 2, 5, 2, 3, 0, 5, 2, 1, 4,
## 4, 0, 3, 0, 0, 3, 1, 4, 2, 0, 4, 4, 3, 1, 0, 9, 0, 0, 5, 1, 3,
## 4, 2, 3, 3, 1, 3, 9, 2, 3, 5, 5, 2, 3, 0, 0, 1, 3, 5, 3, 6, 0,
## 5, 2, 2, 4, 2, 0, 3, 0, 2, 0, 0, 0, 4, 4, 0, 0, 3, 3, 0, 6, 6,
## 1, 1, 5, 1, 2, 3, 2, 4, 5, 3, 1, 0, 0, 0, 7, 0, 0, 3, 0, 5, 6,
## 2, 5, 0, 2, 5, 2, 4, 5, 4, 5, 0, 4, 4, 2, 0, 2, 1, 1, 0, 3, 2,
## 7, 1, 5, 2, 3, 6, 0, 5, 6, 6, 1, 0, 1, 2, 1, 7, 4, 6, 8, 0, 2,
## 3, 4, 0, 3, 5, 0, 5, 7, 6, 3, 5, 2, 0, 6, 0, 0, 0, 2, 4, 2, 0,
## 4, 0, 5, 3, 5, 2, 2, 2, 3, 5), c(4, 0, 5, 5, 0, 2, 3, 5, 2, 3,
## 3, 4, 4, 2, 3, 5, 1, 6, 2, 4, 5, 6, 1, 5, 5, 4, 3, 2, 0, 3, 3,
## 4, 2, 3, 5, 4, 6, 7, 0, 5, 5, 4, 2, 2, 5, 4, 3, 4, 4, 4, 3, 3,
## 3, 3, 2, 4, 5, 4, 3, 2, 3, 4, 2, 4, 3, 6, 5, 5, 7, 8, 5, 4, 3,
## 5, 0, 4, 4, 5, 3, 3, 5, 5, 0, 4, 2, 5, 3, 5, 3, 7, 6, 0, 4, 5,
## 3, 0, 4, 5, 5, 3, 5, 6, 6, 5, 2, 4, 0, 3, 5, 4, 3, 2, 5, 4, 5,
## 2, 5, 0, 0, 2, 3, 4, 5, 5, 4, 3, 3, 3, 3, 2, 2, 4, 4, 2, 3, 2,
## 3, 3, 3, 3, 3, 4, 1, 2, 6, 6, 5, 2, 6, 5, 3, 4, 3, 5, 4, 3, 2,
## 4, 1, 4, 4, 3, 6, 1, 2, 2, 5, 2, 0, 3, 4, 5, 4, 2, 5, 7, 3, 1,
## 4, 4, 3, 5, 7, 9, 3, 3, 7, 2, 3, 3, 3, 3, 4, 5, 4, 4, 5, 9, 5,
## 4, 6, 0, 2, 2, 4, 8, 4, 3, 1, 2, 2, 5, 4, 3, 6, 5, 0, 2, 3, 2,
## 8, 4, 4, 3, 3, 3, 0, 4, 2, 3, 2, 4, 3, 0, 9, 4, 5, 2, 1, 3, 3,
## 3, 3, 5, 4, 0, 1, 4, 5, 2, 4, 0, 5, 4, 7, 4, 3, 2, 2, 4, 0, 3,
## 1, 4, 1, 3, 3, 2, 3, 4, 4, 4, 5, 3, 3, 3, 2, 5, 4, 4, 7, 4, 3,
## 3, 0, 4, 5, 2, 5, 4, 5, 2, 1, 2, 0, 2, 7, 2, 2, 8, 5, 3, 5, 5,
## 2, 4, 2, 4, 2, 2, 6, 0, 4, 5, 3, 2, 4, 2, 5, 0, 3, 3, 4, 3, 5,
## 4, 3, 3, 3, 2, 4, 4, 0, 0, 3, 1, 7, 4, 7, 3, 3, 2, 2, 5, 2, 3,
## 5, 0, 4, 4, 2, 0, 3, 2, 3, 2, 9, 3, 3, 5, 5, 2, 0, 5, 2, 3, 2,
## 3, 8, 4, 5, 4, 0, 3, 3, 9, 4, 5, 2, 4, 4, 4, 5, 5, 4, 0, 3, 2,
## 3, 0, 0, 4, 5, 4, 5, 2, 4, 2, 3, 5, 2, 2, 0, 4, 4, 4, 4, 4, 9,
## 2, 4, 3, 0, 1, 2, 2, 0, 0, 3, 3, 2, 2, 2, 3, 5, 3, 3, 0, 3, 3,
## 6, 5, 4, 7, 9, 4, 3, 4, 5, 0, 1, 4, 1, 7, 2, 3, 5, 6, 0, 4, 2,
## 3, 0, 2, 2, 5, 3, 9, 3, 3, 3, 3, 5, 4, 3, 3, 5, 2, 3, 4, 5, 5,
## 4, 3, 3, 2, 3, 2, 7, 1, 2, 3, 0, 5, 5, 4, 2, 3, 1, 2, 5, 3, 7,
## 2, 2, 3, 3, 3, 5, 2, 6, 4, 4, 0, 4, 8, 5, 7, 4, 0, 2, 2, 5, 5,
## 3, 5, 5, 1, 2, 7, 6, 4, 2, 6, 4, 7, 0, 4, 4, 5, 3, 3, 3, 4, 4,
## 2, 2, 5, 0, 6, 4, 5, 2, 5, 0, 9, 7, 0, 0, 2, 4, 3, 4, 2, 0, 6,
## 0, 3, 5, 5, 1, 4, 5, 7, 0, 6, 4, 3, 5, 6, 5, 4, 3, 2, 1, 3, 3,
## 4, 3, 5, 2, 4, 4, 2, 0, 6, 5, 8, 9, 1, 3, 0, 4, 4, 1, 9, 5, 2,
## 5, 4, 4, 6, 6, 4, 4, 3, 3, 3, 3, 4, 3, 4, 9, 2, 6, 5, 4, 5, 4,
## 2, 3, 4, 3, 4, 3, 3, 2, 4, 0, 4, 2, 4, 4, 5, 4, 1, 9, 3, 5, 3,
## 1, 3, 6, 2, 3, 5, 4, 4, 6, 4, 4, 5, 2, 3, 6, 4, 2, 6, 2, 4, 3,
## 2, 2, 3, 5, 4, 3, 4, 5, 7, 4, 2, 4, 3, 5, 3, 4, 1, 6, 4, 3, 0,
## 3, 7, 2, 3, 4, 5, 4, 6, 4, 2, 3, 2, 1, 5, 1, 3, 2, 6, 4, 4, 3,
## 6, 4, 3, 0, 5, 6, 7, 1, 2, 7, 5, 3, 2, 4, 1, 6, 2, 1, 5, 2, 5,
## 5, 7, 6, 3, 1, 3, 5, 6, 6, 2, 3, 2, 4, 5, 2, 6, 3, 4, 4, 5, 5,
## 3, 0, 0, 5, 6, 4, 2, 2, 4, 7, 5, 4, 2, 3, 4, 5, 5, 5, 5, 2, 2,
## 4, 1, 3, 4, 4, 5, 4, 4, 0, 3, 5, 5, 2, 5, 4, 0, 3, 7, 3, 4, 3,
## 3, 3, 5, 4, 5, 4, 2, 2, 3, 4, 3, 1, 2, 6, 7, 2, 0, 3, 0, 2, 3,
## 7, 2, 1, 0, 0, 6, 6, 4, 0, 4, 9, 3, 0, 6, 2, 3, 4, 1, 2, 5, 0,
## 3, 4, 0, 3, 5, 0, 4, 4, 4, 4, 3, 7, 3, 5, 2, 6, 5, 1, 5, 3, 6,
## 2, 2, 8, 5, 2, 5, 4, 5, 0, 4, 0, 2, 2, 2, 4, 4, 4, 4, 2, 4, 0,
## 4, 4, 2, 4, 3, 1, 4, 0, 4, 6, 4, 4, 2, 5, 2, 7, 4, 3, 4, 7, 4,
## 0, 5, 5, 6, 1, 4, 4, 2, 0, 5, 4, 2, 3, 2, 6, 5, 3, 1, 4, 6, 3,
## 4, 4, 3, 5, 8, 1, 0, 2, 6, 4, 4, 4, 3, 2, 4, 3, 1, 5, 2, 4, 0,
## 3, 3, 4, 7, 3, 3, 0, 9, 4, 3, 4, 3, 2, 5, 2, 4, 4, 6, 3, 0, 5,
## 3, 3, 3, 1, 5, 6, 4, 2, 2, 5, 3, 1, 4, 4, 5, 0, 4, 4, 5, 5, 4,
## 0, 3, 3, 3, 4, 0, 3, 4, 2, 6, 4, 3, 4, 4, 5, 9, 3, 6, 4, 4, 2,
## 4, 3, 3), c(5, 5, 0, 3, 9, 3, 3, 3, 1, 3, 2, 3, 3, 4, 3, 3, 6,
## 3, 6, 0, 2, 0, 8, 4, 4, 5, 3, 4, 0, 2, 2, 2, 4, 3, 4, 3, 3, 1,
## 2, 2, 0, 3, 4, 3, 3, 1, 2, 0, 3, 2, 0, 2, 3, 2, 7, 5, 2, 4, 2,
## 2, 2, 2, 3, 2, 0, 3, 2, 4, 2, 0, 0, 2, 4, 4, 5, 4, 1, 4, 4, 6,
## 4, 0, 3, 5, 4, 1, 3, 4, 3, 2, 0, 9, 5, 2, 3, 7, 3, 4, 3, 1, 2,
## 3, 3, 1, 3, 0, 9, 3, 0, 5, 4, 3, 3, 4, 4, 1, 2, 9, 9, 2, 1, 5,
## 4, 3, 5, 0, 3, 6, 2, 1, 7, 3, 1, 0, 6, 3, 3, 3, 3, 3, 3, 4, 6,
## 4, 3, 1, 3, 4, 3, 4, 5, 4, 1, 1, 4, 1, 4, 4, 1, 3, 1, 2, 0, 8,
## 3, 0, 2, 3, 4, 4, 2, 1, 3, 7, 2, 2, 5, 6, 2, 4, 4, 2, 0, 0, 3,
## 1, 0, 3, 3, 5, 4, 3, 0, 2, 2, 3, 0, 0, 2, 4, 2, 4, 5, 4, 5, 0,
## 3, 2, 1, 5, 5, 0, 3, 4, 3, 3, 3, 4, 6, 3, 0, 3, 5, 1, 2, 1, 4,
## 1, 2, 3, 4, 5, 3, 0, 0, 4, 4, 3, 0, 4, 4, 3, 0, 2, 5, 7, 4, 2,
## 3, 0, 1, 7, 1, 2, 2, 2, 1, 1, 3, 4, 0, 6, 4, 0, 1, 5, 3, 2, 4,
## 4, 5, 4, 2, 2, 3, 0, 1, 1, 3, 3, 0, 2, 3, 3, 9, 1, 3, 4, 2, 2,
## 4, 0, 3, 3, 9, 1, 0, 4, 0, 0, 2, 4, 2, 2, 3, 4, 2, 5, 5, 4, 0,
## 1, 3, 4, 3, 6, 2, 4, 2, 7, 0, 2, 5, 4, 0, 3, 2, 1, 4, 5, 3, 2,
## 9, 8, 2, 4, 0, 2, 1, 4, 4, 0, 3, 3, 6, 0, 4, 8, 5, 3, 3, 7, 6,
## 0, 2, 5, 0, 1, 3, 1, 4, 4, 9, 2, 3, 0, 0, 5, 0, 3, 0, 1, 9, 1,
## 5, 0, 2, 4, 2, 5, 5, 2, 4, 3, 4, 7, 4, 7, 2, 3, 3, 4, 0, 4, 4,
## 7, 5, 3, 2, 2, 0, 0, 9, 4, 4, 4, 3, 4, 0, 3, 2, 2, 0, 3, 2, 6,
## 4, 5, 1, 2, 0, 4, 4, 3, 3, 2, 4, 5, 1, 3, 0, 1, 0, 0, 0, 5, 2,
## 4, 4, 7, 5, 4, 4, 0, 3, 3, 0, 3, 0, 2, 3, 4, 0, 3, 7, 2, 2, 0,
## 3, 3, 5, 4, 0, 2, 2, 4, 3, 1, 4, 2, 2, 0, 0, 3, 3, 5, 3, 3, 1,
## 0, 1, 3, 4, 1, 1, 4, 0, 0, 1, 0, 3, 3, 1, 6, 3, 5, 4, 1, 1, 3,
## 2, 0, 3, 4, 3, 1, 3, 2, 0, 4, 7, 3, 4, 4, 4, 1, 2, 1, 1, 1, 1,
## 0, 4, 2, 0, 2, 7, 2, 3, 2, 3, 4, 2, 1, 5, 1, 5, 4, 5, 3, 4, 2,
## 0, 2, 7, 0, 2, 6, 0, 5, 3, 4, 0, 3, 5, 0, 5, 2, 4, 2, 4, 0, 2,
## 0, 5, 3, 3, 2, 2, 0, 2, 2, 1, 4, 7, 5, 5, 5, 4, 2, 3, 4, 3, 4,
## 1, 3, 2, 1, 0, 0, 3, 9, 2, 4, 5, 0, 4, 4, 4, 2, 5, 3, 2, 4, 0,
## 5, 0, 3, 4, 2, 3, 4, 0, 3, 1, 4, 1, 0, 5, 2, 1, 3, 1, 4, 2, 3,
## 3, 1, 0, 5, 3, 0, 4, 3, 1, 0, 0, 4, 4, 1, 6, 4, 3, 1, 3, 4, 4,
## 4, 0, 1, 4, 1, 3, 4, 3, 3, 6, 1, 5, 0, 2, 4, 3, 4, 0, 3, 4, 0,
## 3, 2, 2, 5, 2, 5, 4, 2, 3, 1, 3, 2, 3, 5, 6, 1, 6, 3, 4, 3, 0,
## 0, 0, 2, 2, 2, 0, 4, 8, 1, 3, 3, 0, 3, 4, 3, 3, 4, 2, 3, 3, 2,
## 1, 1, 2, 0, 1, 5, 0, 8, 0, 5, 1, 4, 2, 3, 5, 0, 1, 2, 5, 1, 3,
## 1, 2, 2, 2, 1, 4, 3, 4, 2, 1, 5, 1, 0, 3, 1, 4, 9, 2, 3, 4, 3,
## 1, 1, 0, 2, 2, 5, 2, 4, 4, 3, 4, 4, 3, 0, 1, 5, 4, 5, 3, 4, 4,
## 4, 0, 1, 0, 1, 6, 2, 4, 9, 1, 2, 4, 3, 4, 1, 3, 0, 2, 1, 2, 0,
## 1, 0, 0, 3, 4, 5, 3, 0, 0, 3, 5, 4, 3, 1, 2, 2, 4, 8, 7, 0, 3,
## 4, 3, 5, 0, 3, 9, 3, 0, 1, 0, 4, 6, 4, 4, 3, 3, 3, 3, 0, 5, 0,
## 4, 2, 5, 2, 1, 5, 1, 3, 3, 2, 5, 3, 3, 3, 3, 5, 1, 0, 3, 2, 4,
## 4, 0, 2, 4, 2, 5, 4, 2, 4, 3, 3, 4, 3, 0, 3, 3, 1, 0, 4, 2, 5,
## 9, 2, 0, 0, 2, 2, 4, 2, 1, 3, 2, 3, 0, 3, 5, 2, 4, 3, 4, 1, 2,
## 7, 9, 2, 3, 5, 1, 1, 2, 4, 2, 8, 3, 0, 3, 1, 0, 3, 3, 1, 8, 8,
## 1, 3, 5, 3, 5, 2, 2, 4, 2, 3, 3, 2, 4, 5, 1, 3, 0, 2, 2, 3, 7,
## 0, 3, 4, 3, 3, 3, 2, 0, 4, 1, 2, 3, 3, 4, 1, 1, 0, 5, 4, 2, 3,
## 6, 1, 0, 0, 1, 4, 4, 0, 5, 4, 3, 0, 3, 0, 2, 0, 4, 2, 3, 8, 0,
## 5, 5, 3, 4, 2, 3, 5, 0, 0, 2, 1, 0, 4, 5, 3, 3, 0), c(0, 2, 0,
## 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1,
## 1, 1, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 4, 0, 1, 2, 0, 2, 0,
## 1, 0, 0, 0, 0, 1, 1, 0, 3, 0, 0, 0, 0, 1, 0, 0, 5, 0, 0, 1, 2,
## 0, 0, 0, 3, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 0, 0, 1, 3, 0, 0, 3,
## 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 1, 1, 2, 0, 2, 0, 0, 2, 4, 1, 1, 3, 0, 0, 0, 0, 1, 0, 0,
## 1, 1, 0, 0, 0, 3, 0, 1, 0, 1, 0, 4, 0, 0, 3, 0, 2, 1, 5, 0, 0,
## 1, 2, 0, 2, 0, 1, 3, 0, 0, 3, 2, 0, 0, 0, 1, 2, 2, 2, 1, 3, 4,
## 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 3, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1,
## 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 1, 3, 4, 0, 1, 1, 1, 0, 2, 0,
## 0, 1, 0, 0, 4, 3, 2, 2, 0, 0, 0, 2, 5, 2, 0, 0, 1, 2, 1, 1, 0,
## 0, 0, 0, 1, 1, 4, 0, 4, 0, 3, 0, 1, 1, 2, 1, 0, 0, 2, 2, 2, 0,
## 0, 0, 0, 1, 2, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 3, 0, 0, 2,
## 3, 0, 1, 0, 2, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1,
## 0, 0, 0, 4, 0, 2, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 1,
## 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 0, 2,
## 0, 1, 0, 0, 2, 0, 1, 0, 1, 1, 0, 0, 0, 3, 0, 0, 3, 0, 1, 0, 0,
## 0, 0, 0, 2, 0, 2, 0, 2, 4, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1,
## 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 9, 5, 1, 1, 2, 0, 0, 0, 0, 1, 2,
## 0, 1, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 0, 5, 1, 0, 2, 4, 0, 5, 0,
## 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 1, 0, 1, 1, 2, 1, 0, 0, 1,
## 3, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 5, 2, 3, 1,
## 0, 0, 4, 0, 0, 1, 0, 2, 1, 1, 2, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0,
## 0, 5, 2, 0, 1, 0, 0, 2, 1, 2, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 1,
## 1, 1, 1, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0,
## 2, 2, 0, 0, 2, 0, 1, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 2, 0,
## 0, 0, 0, 0, 1, 1, 0, 0, 3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 4, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1,
## 0, 2, 0, 0, 1, 0, 0, 2, 1, 1, 1, 0, 5, 0, 2, 1, 0, 0, 2, 0, 0,
## 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 1,
## 0, 2, 0, 0, 2, 0, 1, 3, 1, 1, 0, 2, 2, 3, 0, 0, 1, 2, 0, 2, 0,
## 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 1, 1, 4, 0,
## 0, 0, 2, 0, 0, 1, 3, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0,
## 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0,
## 2, 1, 2, 0, 0, 0, 2, 1, 5, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1,
## 1, 0, 0, 0, 0, 3, 0, 1, 4, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 2, 2,
## 0, 0, 0, 0, 2, 1, 2, 0, 1, 0, 0, 1, 0, 2, 0, 0, 5, 2, 2, 0, 0,
## 2, 0, 0, 1, 5, 0, 1, 0, 0, 5, 1, 1, 0, 0, 1, 0, 0, 0, 3, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0,
## 0, 0, 1, 4, 1, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 4, 5, 0, 2, 0,
## 0, 1, 0, 0, 3, 1, 0, 1, 1, 1, 0, 2, 4, 0, 0, 4, 0, 0, 1, 1, 0,
## 1, 0, 1, 0, 1, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 1, 1, 3, 1, 0,
## 1, 0, 0, 0, 1, 0, 2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0,
## 1, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 3, 2, 4, 2, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0,
## 2, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 1, 2), c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
## 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 2, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
## 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,
## 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 2,
## 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0,
## 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0,
## 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0,
## 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 2, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0,
## 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,
## 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1,
## 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
## 4, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0), c(4, 5, 3, 4, 6, 3, 3, 3, 2, 4, 8, 3, 3, 4, 3, 3, 5,
## 4, 4, 3, 3, 3, 5, 4, 4, 4, 5, 3, 1, 3, 3, 3, 4, 3, 4, 3, 4, 3,
## 3, 3, 3, 4, 5, 4, 4, 3, 3, 2, 4, 3, 3, 3, 4, 4, 4, 4, 3, 4, 3,
## 6, 3, 3, 8, 3, 3, 4, 3, 4, 4, 3, 3, 3, 4, 4, 6, 4, 3, 5, 4, 5,
## 4, 3, 8, 4, 3, 3, 5, 4, 3, 4, 5, 5, 4, 4, 6, 6, 3, 5, 4, 3, 3,
## 4, 4, 3, 5, 2, 6, 5, 3, 4, 5, 3, 3, 6, 4, 2, 3, 4, 4, 2, 3, 4,
## 4, 3, 4, 2, 3, 4, 3, 3, 5, 3, 3, 4, 5, 5, 4, 3, 5, 6, 3, 4, 6,
## 3, 4, 3, 3, 8, 3, 4, 5, 5, 2, 3, 4, 6, 4, 4, 2, 4, 3, 6, 2, 5,
## 5, 2, 4, 5, 7, 4, 3, 3, 4, 4, 4, 3, 5, 6, 3, 4, 5, 4, 3, 3, 4,
## 2, 4, 4, 4, 4, 7, 7, 3, 3, 4, 4, 3, 3, 3, 4, 3, 2, 6, 4, 5, 3,
## 5, 3, 2, 4, 4, 2, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 2, 3, 6, 7,
## 2, 3, 3, 3, 5, 5, 1, 3, 5, 4, 3, 5, 5, 5, 5, 2, 3, 4, 6, 7, 4,
## 3, 2, 3, 6, 2, 4, 4, 3, 2, 2, 5, 4, 5, 5, 6, 3, 4, 4, 4, 3, 5,
## 4, 4, 3, 4, 4, 5, 2, 3, 2, 3, 3, 4, 3, 3, 3, 5, 4, 4, 3, 3, 3,
## 4, 6, 3, 5, 6, 3, 4, 6, 2, 3, 3, 5, 3, 6, 4, 4, 2, 4, 4, 5, 2,
## 1, 4, 4, 4, 4, 3, 4, 3, 5, 2, 6, 4, 5, 2, 4, 8, 3, 3, 4, 4, 3,
## 5, 5, 2, 5, 4, 3, 3, 5, 5, 2, 3, 3, 4, 2, 4, 5, 4, 3, 5, 6, 4,
## 2, 3, 4, 3, 3, 4, 4, 4, 3, 5, 3, 8, 2, 2, 4, 3, 4, 3, 2, 6, 5,
## 4, 3, 5, 4, 3, 4, 4, 3, 4, 3, 5, 5, 5, 4, 3, 9, 3, 3, 3, 4, 4,
## 5, 4, 4, 3, 3, 2, 4, 6, 4, 4, 4, 4, 4, 3, 3, 4, 3, 0, 7, 3, 5,
## 5, 0, 2, 3, 2, 3, 5, 3, 4, 3, 4, 5, 2, 4, 3, 4, 2, 4, 3, 4, 7,
## 4, 4, 5, 6, 4, 7, 3, 4, 3, 3, 4, 2, 3, 3, 5, 1, 4, 5, 3, 3, 3,
## 4, 4, 6, 5, 3, 3, 4, 6, 3, 2, 6, 3, 4, 3, 2, 4, 4, 4, 6, 3, 3,
## 1, 2, 3, 8, 4, 4, 4, 2, 2, 6, 2, 3, 4, 3, 6, 4, 5, 6, 3, 4, 4,
## 3, 2, 4, 4, 4, 3, 3, 4, 6, 5, 5, 3, 4, 4, 5, 3, 4, 2, 2, 3, 3,
## 3, 5, 3, 3, 3, 5, 4, 4, 3, 3, 4, 3, 3, 5, 2, 6, 4, 8, 4, 4, 3,
## 6, 3, 5, 3, 3, 4, 0, 6, 5, 3, 2, 4, 3, 3, 4, 3, 4, 3, 5, 2, 3,
## 3, 4, 4, 4, 3, 4, 3, 3, 3, 2, 4, 6, 4, 5, 4, 7, 4, 3, 4, 4, 3,
## 1, 4, 3, 3, 3, 3, 4, 6, 3, 4, 7, 4, 4, 6, 4, 4, 4, 3, 3, 4, 2,
## 4, 2, 3, 5, 3, 3, 4, 3, 8, 3, 4, 3, 2, 4, 4, 2, 4, 3, 4, 7, 3,
## 4, 3, 1, 4, 8, 2, 3, 3, 3, 2, 3, 7, 4, 2, 5, 4, 4, 2, 3, 4, 4,
## 5, 3, 3, 4, 2, 4, 4, 4, 4, 4, 3, 6, 2, 3, 6, 3, 3, 2, 4, 5, 4,
## 3, 4, 4, 6, 3, 5, 4, 3, 4, 2, 4, 6, 5, 5, 4, 3, 6, 4, 4, 4, 2,
## 3, 2, 2, 3, 2, 5, 4, 5, 2, 4, 4, 2, 3, 7, 4, 3, 5, 2, 3, 4, 3,
## 2, 2, 4, 3, 2, 6, 2, 5, 3, 4, 2, 4, 3, 4, 4, 3, 3, 4, 6, 3, 4,
## 5, 3, 3, 3, 2, 4, 3, 5, 4, 4, 4, 3, 3, 5, 2, 7, 6, 3, 4, 3, 3,
## 2, 3, 4, 3, 3, 4, 3, 4, 4, 3, 4, 4, 5, 2, 3, 7, 4, 4, 3, 4, 4,
## 4, 2, 3, 4, 3, 6, 4, 4, 5, 2, 3, 5, 4, 5, 2, 4, 3, 3, 3, 3, 6,
## 2, 3, 6, 5, 4, 4, 4, 4, 1, 3, 5, 8, 2, 3, 3, 3, 6, 5, 6, 3, 4,
## 5, 3, 5, 4, 5, 6, 4, 2, 2, 3, 6, 4, 4, 4, 3, 3, 3, 4, 3, 5, 2,
## 4, 3, 4, 3, 3, 5, 3, 3, 4, 3, 7, 4, 3, 4, 4, 4, 3, 2, 3, 3, 5,
## 4, 2, 6, 7, 3, 5, 4, 3, 5, 3, 3, 6, 3, 2, 4, 3, 4, 3, 5, 6, 5,
## 4, 6, 3, 2, 4, 2, 4, 3, 3, 4, 3, 4, 5, 3, 0, 3, 4, 4, 7, 3, 3,
## 5, 5, 3, 4, 6, 2, 2, 4, 4, 3, 5, 4, 3, 5, 3, 2, 4, 3, 3, 5, 5,
## 2, 4, 4, 4, 4, 3, 2, 5, 3, 7, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 5,
## 4, 4, 7, 5, 7, 5, 3, 1, 4, 2, 3, 3, 3, 4, 2, 2, 3, 6, 4, 4, 3,
## 5, 2, 3, 2, 2, 5, 4, 4, 4, 5, 3, 2, 5, 3, 2, 2, 4, 3, 4, 5, 2,
## 4, 6, 4, 4, 3, 4, 5, 2, 3, 3, 3, 2, 4, 4, 4, 4, 4), c(3, 4, 4,
## 4, 3, 3, 5, 3, 3, 7, 7, 4, 3, 4, 3, 3, 4, 2, 6, 1, 3, 3, 6, 6,
## 6, 3, 4, 3, 1, 3, 2, 3, 3, 4, 6, 7, 6, 4, 5, 3, 2, 6, 7, 3, 6,
## 4, 3, 4, 5, 3, 3, 1, 2, 6, 3, 5, 6, 7, 5, 2, 2, 3, 6, 3, 6, 3,
## 3, 6, 3, 3, 4, 1, 1, 7, 6, 6, 4, 6, 6, 6, 6, 6, 8, 4, 3, 4, 8,
## 5, 3, 4, 4, 7, 6, 1, 5, 6, 5, 4, 3, 2, 3, 8, 3, 6, 4, 2, 6, 4,
## 4, 3, 7, 3, 3, 6, 3, 3, 6, 3, 7, 3, 5, 5, 6, 4, 8, 2, 3, 6, 1,
## 3, 7, 4, 4, 7, 6, 3, 3, 3, 8, 6, 1, 6, 6, 4, 3, 3, 1, 7, 3, 7,
## 7, 6, 4, 7, 8, 4, 8, 5, 1, 5, 2, 4, 1, 3, 4, 5, 3, 5, 5, 4, 4,
## 6, 4, 3, 6, 3, 4, 7, 3, 4, 8, 4, 8, 6, 3, 1, 4, 3, 4, 6, 3, 3,
## 1, 6, 3, 5, 4, 5, 5, 3, 2, 5, 8, 5, 7, 4, 2, 6, 3, 4, 2, 3, 4,
## 3, 3, 3, 3, 8, 6, 5, 1, 2, 3, 3, 2, 4, 8, 6, 4, 3, 6, 7, 3, 1,
## 4, 7, 1, 5, 5, 7, 7, 8, 3, 5, 5, 4, 8, 3, 3, 3, 5, 6, 1, 4, 3,
## 5, 3, 1, 5, 3, 6, 8, 5, 6, 3, 4, 3, 1, 8, 4, 3, 3, 3, 1, 8, 3,
## 4, 2, 2, 4, 2, 7, 6, 3, 4, 4, 6, 6, 3, 4, 6, 4, 2, 6, 6, 3, 2,
## 7, 1, 4, 3, 7, 5, 3, 3, 3, 3, 5, 8, 8, 3, 1, 5, 6, 6, 6, 3, 8,
## 5, 7, 4, 3, 3, 8, 3, 5, 7, 1, 5, 2, 3, 3, 4, 4, 1, 8, 4, 3, 4,
## 8, 8, 1, 3, 2, 4, 4, 6, 8, 5, 7, 5, 3, 8, 5, 3, 4, 7, 6, 7, 6,
## 3, 6, 4, 4, 6, 1, 1, 7, 4, 3, 7, 1, 6, 4, 4, 7, 5, 1, 1, 5, 5,
## 3, 6, 3, 6, 3, 6, 3, 5, 8, 6, 5, 6, 3, 6, 7, 4, 3, 2, 3, 1, 3,
## 4, 6, 3, 3, 6, 6, 6, 6, 4, 4, 7, 8, 4, 7, 8, 8, 2, 7, 2, 2, 8,
## 6, 8, 1, 4, 7, 3, 6, 3, 3, 1, 2, 4, 3, 4, 3, 2, 8, 8, 4, 8, 1,
## 3, 3, 4, 6, 3, 3, 2, 7, 1, 3, 8, 5, 3, 4, 2, 1, 6, 5, 5, 3, 4,
## 3, 3, 3, 7, 3, 4, 3, 4, 4, 3, 5, 7, 2, 1, 1, 1, 6, 7, 3, 2, 4,
## 2, 3, 6, 3, 3, 8, 1, 7, 2, 2, 7, 6, 3, 3, 2, 3, 3, 3, 7, 5, 4,
## 3, 3, 3, 7, 6, 3, 1, 6, 5, 3, 3, 3, 5, 5, 1, 6, 2, 5, 5, 8, 1,
## 4, 1, 1, 3, 2, 5, 6, 3, 2, 6, 8, 8, 5, 3, 4, 3, 2, 4, 5, 3, 2,
## 8, 5, 3, 6, 3, 4, 3, 4, 3, 3, 6, 7, 3, 3, 4, 2, 6, 6, 3, 3, 2,
## 6, 4, 2, 3, 8, 5, 8, 3, 3, 1, 3, 8, 6, 6, 1, 6, 4, 5, 4, 3, 1,
## 6, 4, 1, 8, 6, 6, 8, 3, 4, 8, 3, 4, 5, 2, 7, 4, 3, 8, 5, 3, 6,
## 7, 6, 5, 4, 4, 3, 5, 6, 5, 4, 1, 4, 4, 3, 3, 1, 1, 6, 6, 5, 4,
## 3, 6, 1, 4, 7, 6, 2, 8, 3, 2, 1, 2, 6, 4, 3, 8, 3, 6, 2, 3, 1,
## 3, 1, 4, 5, 3, 3, 2, 7, 4, 6, 3, 1, 7, 8, 1, 4, 2, 8, 3, 8, 6,
## 6, 3, 3, 7, 1, 8, 5, 7, 1, 7, 4, 6, 2, 5, 2, 3, 2, 2, 5, 5, 7,
## 6, 1, 3, 6, 1, 3, 7, 7, 3, 6, 2, 3, 6, 1, 5, 1, 3, 4, 1, 8, 3,
## 6, 3, 3, 5, 3, 1, 3, 5, 3, 3, 2, 7, 3, 1, 6, 2, 1, 1, 1, 4, 1,
## 8, 8, 1, 8, 1, 4, 7, 1, 6, 6, 1, 3, 3, 2, 3, 3, 2, 4, 3, 4, 3,
## 1, 6, 2, 1, 5, 5, 3, 6, 7, 4, 3, 3, 3, 6, 4, 3, 3, 3, 6, 6, 3,
## 5, 7, 3, 6, 8, 6, 6, 3, 6, 4, 1, 4, 3, 2, 1, 3, 3, 7, 4, 8, 7,
## 4, 5, 8, 7, 7, 2, 1, 1, 4, 8, 6, 3, 3, 7, 7, 4, 6, 5, 8, 4, 4,
## 3, 4, 1, 6, 4, 6, 3, 3, 3, 5, 5, 4, 7, 3, 4, 6, 4, 3, 1, 7, 7,
## 2, 8, 2, 7, 4, 4, 3, 3, 4, 3, 3, 5, 6, 7, 6, 3, 6, 6, 2, 8, 8,
## 3, 6, 7, 2, 6, 3, 8, 3, 3, 1, 3, 8, 8, 4, 7, 5, 2, 4, 4, 4, 3,
## 4, 1, 6, 6, 1, 3, 5, 3, 5, 3, 8, 8, 1, 3, 8, 4, 1, 5, 8, 3, 3,
## 8, 3, 2, 6, 3, 8, 3, 1, 6, 1, 4, 3, 3, 6, 3, 3, 5, 5, 6, 3, 1,
## 7, 6, 8, 3, 1, 4, 4, 6, 3, 2, 3, 3, 3, 1, 6, 5, 3, 6, 3, 6, 5,
## 5, 1, 2, 3, 3, 5, 6, 1, 2, 3, 8, 6, 3, 5, 8, 3, 3, 3, 3, 3, 6,
## 3, 2, 3, 7, 1, 7, 3, 2, 1, 6, 3, 6, 8, 1, 4, 8, 6, 4, 3, 5, 4,
## 3, 4, 4, 3, 1, 3, 8, 3, 6, 3), c(0, 2, 2, 0, 0, 0, 0, 0, 0, 2,
## 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2,
## 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 2, 0, 1, 0, 2,
## 0, 1, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0,
## 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2,
## 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0,
## 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2,
## 2, 2, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,
## 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0,
## 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0,
## 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 2, 0, 0,
## 2, 0, 3, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2,
## 1, 0, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0,
## 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0,
## 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0,
## 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 1, 3, 0, 2, 0, 0, 0, 2,
## 2, 0, 2, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0,
## 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1,
## 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0,
## 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 1, 0, 0, 2, 0, 0, 2, 0, 2,
## 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2,
## 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 1, 1, 0, 2,
## 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 2, 2, 0, 3, 0, 0,
## 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2,
## 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2,
## 0, 2, 0, 2, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0,
## 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2,
## 2, 2, 2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0,
## 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0,
## 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0,
## 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2,
## 0, 2, 2, 1, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0,
## 1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0,
## 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0,
## 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 2, 0, 0,
## 2, 0, 2, 1, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 1,
## 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2,
## 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2,
## 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2,
## 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 2, 0, 2, 0, 3, 1, 2, 0,
## 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2,
## 2, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0,
## 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0,
## 1, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0,
## 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2,
## 0, 0, 0), c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0), c(0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0,
## 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 3, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), c(0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1,
## 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1,
## 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1,
## 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1,
## 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1)), control = list(20, 7, 0, 4, 5, 2, 0, 30, 0))
## n= 1000
##
## CP nsplit rel error
## 1 0.008474576 0 1.0000000
## 2 0.007263923 4 0.9661017
## 3 0.000000000 11 0.9152542
##
## Variable importance
## MGODGE MOPLMIDD PPERSAUT APERSAUT MBERMIDD ABRAND MKOOPKLA MINKM30
## 14 8 8 6 5 4 4 4
## MOPLHOOG MINK4575 MOSTYPE MOPLLAAG MGODPR MINK3045 MRELGE MSKB1
## 4 4 3 3 3 3 3 2
## MBERARBG MINKGEM MZFONDS MZPART MOSHOOFD MHHUUR MFALLEEN MHKOOP
## 2 2 2 2 2 2 2 2
## MSKA MFWEKIND MRELSA MBERHOOG PBRAND MAUT2 MBERARBO
## 1 1 1 1 1 1 1
##
## Node number 1: 1000 observations, complexity param=0.008474576
## predicted class=No expected loss=0.059 P(node) =1
## class counts: 941 59
## probabilities: 0.941 0.059
## left son=2 (606 obs) right son=3 (394 obs)
## Primary splits:
## PPERSAUT < 5.5 to the left, improve=3.607985, (0 missing)
## PPLEZIER < 0.5 to the left, improve=3.136790, (0 missing)
## APLEZIER < 0.5 to the left, improve=3.136790, (0 missing)
## MKOOPKLA < 6.5 to the left, improve=1.714118, (0 missing)
## APERSAUT < 0.5 to the left, improve=1.682000, (0 missing)
## Surrogate splits:
## APERSAUT < 0.5 to the left, agree=0.894, adj=0.731, (0 split)
## PBRAND < 3.5 to the left, agree=0.644, adj=0.096, (0 split)
## PLEVEN < 1.5 to the left, agree=0.624, adj=0.046, (0 split)
## ALEVEN < 0.5 to the left, agree=0.623, adj=0.043, (0 split)
## PWAPART < 1.5 to the left, agree=0.620, adj=0.036, (0 split)
##
## Node number 2: 606 observations
## predicted class=No expected loss=0.02475248 P(node) =0.606
## class counts: 591 15
## probabilities: 0.975 0.025
##
## Node number 3: 394 observations, complexity param=0.008474576
## predicted class=No expected loss=0.1116751 P(node) =0.394
## class counts: 350 44
## probabilities: 0.888 0.112
## left son=6 (385 obs) right son=7 (9 obs)
## Primary splits:
## ABRAND < 1.5 to the left, improve=2.039833, (0 missing)
## MBERMIDD < 1.5 to the left, improve=1.864178, (0 missing)
## MKOOPKLA < 6.5 to the left, improve=1.718047, (0 missing)
## MSKD < 2.5 to the right, improve=1.560824, (0 missing)
## MOPLHOOG < 3.5 to the left, improve=1.560413, (0 missing)
##
## Node number 6: 385 observations, complexity param=0.008474576
## predicted class=No expected loss=0.1038961 P(node) =0.385
## class counts: 345 40
## probabilities: 0.896 0.104
## left son=12 (325 obs) right son=13 (60 obs)
## Primary splits:
## MOPLHOOG < 3.5 to the left, improve=1.807799, (0 missing)
## MKOOPKLA < 6.5 to the left, improve=1.580375, (0 missing)
## MBERMIDD < 1.5 to the left, improve=1.496689, (0 missing)
## MSKD < 2.5 to the right, improve=1.355985, (0 missing)
## MINK7512 < 0.5 to the left, improve=1.168095, (0 missing)
## Surrogate splits:
## MSKA < 4.5 to the left, agree=0.896, adj=0.333, (0 split)
## MBERHOOG < 5.5 to the left, agree=0.881, adj=0.233, (0 split)
## MOSTYPE < 1.5 to the right, agree=0.873, adj=0.183, (0 split)
## MZFONDS < 4.5 to the right, agree=0.862, adj=0.117, (0 split)
## MZPART < 4.5 to the left, agree=0.862, adj=0.117, (0 split)
##
## Node number 7: 9 observations
## predicted class=No expected loss=0.4444444 P(node) =0.009
## class counts: 5 4
## probabilities: 0.556 0.444
##
## Node number 12: 325 observations, complexity param=0.007263923
## predicted class=No expected loss=0.08307692 P(node) =0.325
## class counts: 298 27
## probabilities: 0.917 0.083
## left son=24 (61 obs) right son=25 (264 obs)
## Primary splits:
## MBERMIDD < 1.5 to the left, improve=1.0365730, (0 missing)
## MGODGE < 4.5 to the left, improve=1.0210930, (0 missing)
## MSKD < 2.5 to the right, improve=0.8545055, (0 missing)
## MGEMLEEF < 2.5 to the right, improve=0.8239571, (0 missing)
## MFWEKIND < 4.5 to the left, improve=0.6465200, (0 missing)
## Surrogate splits:
## MSKD < 3.5 to the right, agree=0.843, adj=0.164, (0 split)
## MOPLLAAG < 8.5 to the right, agree=0.834, adj=0.115, (0 split)
## MBERBOER < 3.5 to the right, agree=0.828, adj=0.082, (0 split)
## MOPLMIDD < 0.5 to the left, agree=0.825, adj=0.066, (0 split)
## MGODPR < 8.5 to the right, agree=0.822, adj=0.049, (0 split)
##
## Node number 13: 60 observations, complexity param=0.008474576
## predicted class=No expected loss=0.2166667 P(node) =0.06
## class counts: 47 13
## probabilities: 0.783 0.217
## left son=26 (48 obs) right son=27 (12 obs)
## Primary splits:
## MGODGE < 1.5 to the right, improve=4.033333, (0 missing)
## MBERARBG < 1.5 to the left, improve=2.323021, (0 missing)
## MRELGE < 6.5 to the right, improve=2.128030, (0 missing)
## MHHUUR < 0.5 to the right, improve=2.072024, (0 missing)
## MHKOOP < 8.5 to the left, improve=2.072024, (0 missing)
## Surrogate splits:
## MGODPR < 6.5 to the left, agree=0.850, adj=0.250, (0 split)
## MZFONDS < 0.5 to the right, agree=0.833, adj=0.167, (0 split)
## MZPART < 8.5 to the left, agree=0.833, adj=0.167, (0 split)
## MINK4575 < 6.5 to the left, agree=0.833, adj=0.167, (0 split)
## MAUT2 < 3.5 to the left, agree=0.817, adj=0.083, (0 split)
##
## Node number 24: 61 observations
## predicted class=No expected loss=0 P(node) =0.061
## class counts: 61 0
## probabilities: 1.000 0.000
##
## Node number 25: 264 observations, complexity param=0.007263923
## predicted class=No expected loss=0.1022727 P(node) =0.264
## class counts: 237 27
## probabilities: 0.898 0.102
## left son=50 (215 obs) right son=51 (49 obs)
## Primary splits:
## MGODGE < 4.5 to the left, improve=1.7974440, (0 missing)
## MGODOV < 0.5 to the right, improve=1.1791670, (0 missing)
## MBERHOOG < 1.5 to the right, improve=0.9166667, (0 missing)
## MFWEKIND < 4.5 to the left, improve=0.8037207, (0 missing)
## MZFONDS < 6.5 to the left, improve=0.7552197, (0 missing)
## Surrogate splits:
## MGODPR < 2.5 to the right, agree=0.845, adj=0.163, (0 split)
## MINK123M < 2.5 to the left, agree=0.826, adj=0.061, (0 split)
## MINKGEM < 7.5 to the left, agree=0.822, adj=0.041, (0 split)
## MGEMLEEF < 1.5 to the right, agree=0.818, adj=0.020, (0 split)
## MRELOV < 6.5 to the left, agree=0.818, adj=0.020, (0 split)
##
## Node number 26: 48 observations
## predicted class=No expected loss=0.125 P(node) =0.048
## class counts: 42 6
## probabilities: 0.875 0.125
##
## Node number 27: 12 observations
## predicted class=Yes expected loss=0.4166667 P(node) =0.012
## class counts: 5 7
## probabilities: 0.417 0.583
##
## Node number 50: 215 observations, complexity param=0.007263923
## predicted class=No expected loss=0.0744186 P(node) =0.215
## class counts: 199 16
## probabilities: 0.926 0.074
## left son=100 (93 obs) right son=101 (122 obs)
## Primary splits:
## MINK3045 < 3.5 to the left, improve=1.3286350, (0 missing)
## MOSTYPE < 37.5 to the left, improve=1.1766320, (0 missing)
## MOSHOOFD < 8.5 to the left, improve=1.1766320, (0 missing)
## MZPART < 3.5 to the right, improve=0.7092409, (0 missing)
## MZFONDS < 5.5 to the left, improve=0.6889959, (0 missing)
## Surrogate splits:
## MINKM30 < 4.5 to the right, agree=0.679, adj=0.258, (0 split)
## MHHUUR < 5.5 to the right, agree=0.651, adj=0.194, (0 split)
## MHKOOP < 3.5 to the left, agree=0.651, adj=0.194, (0 split)
## MINKGEM < 4.5 to the right, agree=0.651, adj=0.194, (0 split)
## MFALLEEN < 3.5 to the right, agree=0.637, adj=0.161, (0 split)
##
## Node number 51: 49 observations, complexity param=0.007263923
## predicted class=No expected loss=0.2244898 P(node) =0.049
## class counts: 38 11
## probabilities: 0.776 0.224
## left son=102 (42 obs) right son=103 (7 obs)
## Primary splits:
## MKOOPKLA < 6.5 to the left, improve=1.9659860, (0 missing)
## MSKB1 < 0.5 to the left, improve=1.7834470, (0 missing)
## MOSTYPE < 33.5 to the right, improve=1.2468310, (0 missing)
## MBERARBG < 4.5 to the right, improve=0.9636635, (0 missing)
## MINKGEM < 3.5 to the left, improve=0.9312245, (0 missing)
## Surrogate splits:
## MOSTYPE < 12.5 to the right, agree=0.939, adj=0.571, (0 split)
## MOSHOOFD < 2.5 to the right, agree=0.918, adj=0.429, (0 split)
## MFWEKIND < 8.5 to the left, agree=0.898, adj=0.286, (0 split)
## MBERMIDD < 6.5 to the left, agree=0.898, adj=0.286, (0 split)
## MBERARBG < 0.5 to the right, agree=0.898, adj=0.286, (0 split)
##
## Node number 100: 93 observations
## predicted class=No expected loss=0.01075269 P(node) =0.093
## class counts: 92 1
## probabilities: 0.989 0.011
##
## Node number 101: 122 observations, complexity param=0.007263923
## predicted class=No expected loss=0.1229508 P(node) =0.122
## class counts: 107 15
## probabilities: 0.877 0.123
## left son=202 (78 obs) right son=203 (44 obs)
## Primary splits:
## MINKM30 < 2.5 to the left, improve=1.4979560, (0 missing)
## MOPLHOOG < 2.5 to the left, improve=1.4007460, (0 missing)
## MINK3045 < 4.5 to the right, improve=1.1890870, (0 missing)
## MOPLMIDD < 4.5 to the right, improve=1.1501850, (0 missing)
## MOSTYPE < 33.5 to the left, improve=0.8465403, (0 missing)
## Surrogate splits:
## MINKGEM < 3.5 to the right, agree=0.787, adj=0.409, (0 split)
## MFALLEEN < 2.5 to the left, agree=0.770, adj=0.364, (0 split)
## MHHUUR < 3.5 to the left, agree=0.762, adj=0.341, (0 split)
## MHKOOP < 5.5 to the right, agree=0.754, adj=0.318, (0 split)
## MRELGE < 5.5 to the right, agree=0.721, adj=0.227, (0 split)
##
## Node number 102: 42 observations
## predicted class=No expected loss=0.1666667 P(node) =0.042
## class counts: 35 7
## probabilities: 0.833 0.167
##
## Node number 103: 7 observations
## predicted class=Yes expected loss=0.4285714 P(node) =0.007
## class counts: 3 4
## probabilities: 0.429 0.571
##
## Node number 202: 78 observations
## predicted class=No expected loss=0.06410256 P(node) =0.078
## class counts: 73 5
## probabilities: 0.936 0.064
##
## Node number 203: 44 observations, complexity param=0.007263923
## predicted class=No expected loss=0.2272727 P(node) =0.044
## class counts: 34 10
## probabilities: 0.773 0.227
## left son=406 (12 obs) right son=407 (32 obs)
## Primary splits:
## MOPLMIDD < 4.5 to the right, improve=1.704545, (0 missing)
## MINK3045 < 4.5 to the right, improve=1.572193, (0 missing)
## MINK4575 < 1.5 to the left, improve=1.400715, (0 missing)
## MGODOV < 1.5 to the right, improve=1.174086, (0 missing)
## MOPLLAAG < 4.5 to the left, improve=1.174086, (0 missing)
## Surrogate splits:
## MOPLLAAG < 4.5 to the left, agree=0.932, adj=0.750, (0 split)
## MSKB1 < 2.5 to the right, agree=0.886, adj=0.583, (0 split)
## MBERMIDD < 3.5 to the right, agree=0.864, adj=0.500, (0 split)
## MRELGE < 4.5 to the left, agree=0.818, adj=0.333, (0 split)
## MBERARBG < 0.5 to the left, agree=0.795, adj=0.250, (0 split)
##
## Node number 406: 12 observations
## predicted class=No expected loss=0 P(node) =0.012
## class counts: 12 0
## probabilities: 1.000 0.000
##
## Node number 407: 32 observations, complexity param=0.007263923
## predicted class=No expected loss=0.3125 P(node) =0.032
## class counts: 22 10
## probabilities: 0.688 0.312
## left son=814 (24 obs) right son=815 (8 obs)
## Primary splits:
## MOPLMIDD < 3.5 to the left, improve=2.083333, (0 missing)
## MINK4575 < 1.5 to the left, improve=1.432540, (0 missing)
## PBRAND < 3.5 to the right, improve=1.342157, (0 missing)
## MBERHOOG < 1.5 to the right, improve=1.313636, (0 missing)
## MINK3045 < 4.5 to the right, improve=1.313636, (0 missing)
## Surrogate splits:
## MINK4575 < 2.5 to the left, agree=0.875, adj=0.500, (0 split)
## MGODGE < 3.5 to the left, agree=0.812, adj=0.250, (0 split)
## MRELSA < 1.5 to the left, agree=0.812, adj=0.250, (0 split)
## MRELGE < 7.5 to the left, agree=0.781, adj=0.125, (0 split)
## MBERARBO < 3.5 to the left, agree=0.781, adj=0.125, (0 split)
##
## Node number 814: 24 observations
## predicted class=No expected loss=0.2083333 P(node) =0.024
## class counts: 19 5
## probabilities: 0.792 0.208
##
## Node number 815: 8 observations
## predicted class=Yes expected loss=0.375 P(node) =0.008
## class counts: 3 5
## probabilities: 0.375 0.625
##
## n= 1000
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 1000 59 No (0.94100000 0.05900000)
## 2) PPERSAUT< 5.5 606 15 No (0.97524752 0.02475248) *
## 3) PPERSAUT>=5.5 394 44 No (0.88832487 0.11167513)
## 6) ABRAND< 1.5 385 40 No (0.89610390 0.10389610)
## 12) MOPLHOOG< 3.5 325 27 No (0.91692308 0.08307692)
## 24) MBERMIDD< 1.5 61 0 No (1.00000000 0.00000000) *
## 25) MBERMIDD>=1.5 264 27 No (0.89772727 0.10227273)
## 50) MGODGE< 4.5 215 16 No (0.92558140 0.07441860)
## 100) MINK3045< 3.5 93 1 No (0.98924731 0.01075269) *
## 101) MINK3045>=3.5 122 15 No (0.87704918 0.12295082)
## 202) MINKM30< 2.5 78 5 No (0.93589744 0.06410256) *
## 203) MINKM30>=2.5 44 10 No (0.77272727 0.22727273)
## 406) MOPLMIDD>=4.5 12 0 No (1.00000000 0.00000000) *
## 407) MOPLMIDD< 4.5 32 10 No (0.68750000 0.31250000)
## 814) MOPLMIDD< 3.5 24 5 No (0.79166667 0.20833333) *
## 815) MOPLMIDD>=3.5 8 3 Yes (0.37500000 0.62500000) *
## 51) MGODGE>=4.5 49 11 No (0.77551020 0.22448980)
## 102) MKOOPKLA< 6.5 42 7 No (0.83333333 0.16666667) *
## 103) MKOOPKLA>=6.5 7 3 Yes (0.42857143 0.57142857) *
## 13) MOPLHOOG>=3.5 60 13 No (0.78333333 0.21666667)
## 26) MGODGE>=1.5 48 6 No (0.87500000 0.12500000) *
## 27) MGODGE< 1.5 12 5 Yes (0.41666667 0.58333333) *
## 7) ABRAND>=1.5 9 4 No (0.55555556 0.44444444) *# Plot the tree with optimal cp
rpart.plot(model2$finalModel)
Answer:The model above has 3 CP values listed (0.00847, 0.00726, and 0); with the number of splits has increased from 0-11.As seen the variable importance is the highest for MGODGE(14) followed by MOPLMIDD, PPERSAUT and APERSAUT. The depth of the tree as seen above is 6 (max). The tree has 11(+1) internal nodes, with 13 terminal nodes at the bottom showing the final prediction. The green nodes at the terminal show the “Yes” in the Caravan dataset.
Part C
Fit a random forest model to the data. Using cross-validation, determine the optimal parameters. Briefly explain your rationale.
# Train the Random Forest model using caret
rf_model <- train(Purchase ~ ., data = df.train,
method = "rf",
trControl = control,
tuneGrid = expand.grid(mtry = 1:10), # Tune mtry from 1 to 10
ntree = 500) # Set the number of trees to 500
tunegrid = expand.grid(mtry=1:10)
rf_model = train(Purchase~.,
data=df.train,
method='rf',
tuneGrid=tunegrid,
trControl=trainControl(method="cv", number=5))
# View the results of the cross-validation
print(rf_model)## Random Forest
##
## 1000 samples
## 85 predictor
## 2 classes: 'No', 'Yes'
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 801, 800, 800, 799, 800
## Resampling results across tuning parameters:
##
## mtry Accuracy Kappa
## 1 0.9410044 0.000000000
## 2 0.9410044 0.000000000
## 3 0.9399994 -0.001859679
## 4 0.9369893 -0.006716295
## 5 0.9379944 0.019538096
## 6 0.9369893 0.016874447
## 7 0.9379844 0.046074910
## 8 0.9369893 0.016874447
## 9 0.9369893 0.042470976
## 10 0.9349893 0.012646844
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 1.# Plot the cross-validation results
plot(rf_model)
varImpPlot(rf_model$finalModel,
sort = T,
main = "Variable Importance")
Answer : The Acccuracy column of the model shows the highest when mtry = 3 (0.9419994), though accuracy is aomost around 0.94 for most mtry values. The Kappa values are close to 0 that shows little to no agreement & we are looking for a higher Kappa to indicate a better model, so there is still room for improvement.
Part D
Produce plots that illustrate your choice of parameters.
plot(rf_model)
Part E
What features are the most important for the bagged model? Provide plots to support your response.
varImpPlot(rf_model$finalModel,
sort = T,
main = "Variable Importance", cex = 0.6)
Answer: From the plot, the images at the top of the list are the most important while those are the lower in th elist contribute lesser to the model’s predictive model. The most important being MOSTYPE, MGODGE, followed by MKOOPKLA, with mean decrease in Gini.These features are seemingly the most influential in making predictions. The features at the lower part of the list, may be noisy, or irrelevant to the analysis.
Part F
Apply both models to the testing data. Which model performs best? Provide evidence (e.g., MCR, Confusion Matrix, ROC) to support your conclusion.
#I used AI support to do this comparison
dt_pred <- predict(model2, newdata = df.test)
dt_probs <- predict(model2, newdata = df.test, type = "prob")
# Random Forest predictions
rf_pred <- predict(rf_model, newdata = df.test)
rf_probs <- predict(rf_model, newdata = df.test, type = "prob")
# Calculate Misclassification Rate (MCR)
dt_mcr <- mean(dt_pred != df.test$Purchase)
rf_mcr <- mean(rf_pred != df.test$Purchase)
print(paste("Decision Tree MCR:", round(dt_mcr, 4)))## [1] "Decision Tree MCR: 0.078"print(paste("Random Forest MCR:", round(rf_mcr, 4)))## [1] "Random Forest MCR: 0.0599"# Create confusion matrices
dt_conf_matrix <- confusionMatrix(dt_pred, df.test$Purchase)
rf_conf_matrix <- confusionMatrix(rf_pred, df.test$Purchase)
print("Decision Tree Confusion Matrix:")## [1] "Decision Tree Confusion Matrix:"print(dt_conf_matrix)## Confusion Matrix and Statistics
##
## Reference
## Prediction No Yes
## No 4428 271
## Yes 105 18
##
## Accuracy : 0.922
## 95% CI : (0.9141, 0.9294)
## No Information Rate : 0.9401
## P-Value [Acc > NIR] : 1
##
## Kappa : 0.0535
##
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 0.97684
## Specificity : 0.06228
## Pos Pred Value : 0.94233
## Neg Pred Value : 0.14634
## Prevalence : 0.94007
## Detection Rate : 0.91829
## Detection Prevalence : 0.97449
## Balanced Accuracy : 0.51956
##
## 'Positive' Class : No
## print("Random Forest Confusion Matrix:")## [1] "Random Forest Confusion Matrix:"print(rf_conf_matrix)## Confusion Matrix and Statistics
##
## Reference
## Prediction No Yes
## No 4533 289
## Yes 0 0
##
## Accuracy : 0.9401
## 95% CI : (0.933, 0.9466)
## No Information Rate : 0.9401
## P-Value [Acc > NIR] : 0.5156
##
## Kappa : 0
##
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 1.0000
## Specificity : 0.0000
## Pos Pred Value : 0.9401
## Neg Pred Value : NaN
## Prevalence : 0.9401
## Detection Rate : 0.9401
## Detection Prevalence : 1.0000
## Balanced Accuracy : 0.5000
##
## 'Positive' Class : No
## # ROC curves
dt_roc <- roc(df.test$Purchase, dt_probs[, "Yes"])
rf_roc <- roc(df.test$Purchase, rf_probs[, "Yes"])
# Plot ROC curves
plot(dt_roc, col = "blue", main = "ROC Curves")
plot(rf_roc, col = "red", add = TRUE)
legend("bottomright", legend = c(
paste("Decision Tree (AUC =", round(auc(dt_roc), 3), ")"),
paste("Random Forest (AUC =", round(auc(rf_roc), 3), ")")
), col = c("blue", "red"), lwd = 2)
# Compare AUC values
print(paste("Decision Tree AUC:", round(auc(dt_roc), 4)))## [1] "Decision Tree AUC: 0.5494"print(paste("Random Forest AUC:", round(auc(rf_roc), 4)))## [1] "Random Forest AUC: 0.6133"# Final comparison summary
cat("\nModel Performance Summary:\n")##
## Model Performance Summary:cat("-------------------------\n")## -------------------------cat(sprintf("Decision Tree MCR: %.4f, AUC: %.4f\n", dt_mcr, auc(dt_roc)))## Decision Tree MCR: 0.0780, AUC: 0.5494cat(sprintf("Random Forest MCR: %.4f, AUC: %.4f\n", rf_mcr, auc(rf_roc)))## Random Forest MCR: 0.0599, AUC: 0.6133cat("\nBest model: ", ifelse(auc(rf_roc) > auc(dt_roc), "Random Forest", "Decision Tree"), "\n")##
## Best model: Random ForestAnswer:The model performance summary shows that the Decision Tree MCR is 7.8% with an AUC of 0.5494, suggesting a relatively low ability to predict and poor performance in determining the classes. On the other hand Random Forest has a MCR of 6.08% with an AUC of 0.6852, showing that its has the better ability to identify the two classes and has lower misclassification rate than decision tree. So in comparision, Random forest is the better model than the Decision Tree but both the models are still unable to identify the negatives correctly (i.e poor specificity).