Assignment 7
Jason Villa
2026-07-28
Problem 3
Consider the Gini index, classification error, and entropy in a simple classification setting with two classes. Create a single plot that displays each of these quantities as a function of pˆm1. The x-axis should display pˆm1, ranging from 0 to 1, and the y-axis should display the value of the Gini index, classification error, and entropy. Hint: In a setting with two classes, pˆm1 =1 − pˆm2. You could make this plot by hand, but it will be much easier to make in R
p=seq(0,1,0.0001)
#Gini
G=2*p*(1-p)
#Classification Error
E=1-pmax(p,1-p)
#Entropy
D=-(p*log(p) + (1-p)*log(1-p))
plot(p,D, col="red",ylab="")
lines(p,E,col='green')
lines(p,G,col='blue')
legend(0.3,0.15,c("Entropy", "Missclassification","Gini"),lty=c(1,1,1),lwd=c(2.5,2.5,2.5),col=c('red','green','blue'))
Problem 8
In the lab, a classification tree was applied to the Carseats data set after converting Sales into a qualitative response variable. Now we will seek to predict Sales using regression trees and related approaches, treating the response as a quantitative variable.
- Split the data set into a training set and a test set.
library(ISLR2)## Warning: package 'ISLR2' was built under R version 4.3.3library(caret)## Warning: package 'caret' was built under R version 4.3.3## Loading required package: ggplot2## Loading required package: lattice## Warning: package 'lattice' was built under R version 4.3.3library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.3.3## Warning: package 'tibble' was built under R version 4.3.3## Warning: package 'tidyr' was built under R version 4.3.3## Warning: package 'readr' was built under R version 4.3.3## Warning: package 'dplyr' was built under R version 4.3.3## Warning: package 'lubridate' was built under R version 4.3.3## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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library(rpart.plot)
library(randomForest)## Warning: package 'randomForest' was built under R version 4.3.3## randomForest 4.7-1.2
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## steplibrary(recipes)
data(Carseats)
head(Carseats)## Sales CompPrice Income Advertising Population Price ShelveLoc Age Education
## 1 9.50 138 73 11 276 120 Bad 42 17
## 2 11.22 111 48 16 260 83 Good 65 10
## 3 10.06 113 35 10 269 80 Medium 59 12
## 4 7.40 117 100 4 466 97 Medium 55 14
## 5 4.15 141 64 3 340 128 Bad 38 13
## 6 10.81 124 113 13 501 72 Bad 78 16
## Urban US
## 1 Yes Yes
## 2 Yes Yes
## 3 Yes Yes
## 4 Yes Yes
## 5 Yes No
## 6 No Yestrain_idx <- createDataPartition(Carseats$Sales, p = .8, list = FALSE)
train_df <- Carseats[train_idx, ]
test_df <- Carseats[-train_idx, ]- Fit a regression tree to the training set. Plot the tree, and interpret the results. What test MSE do you obtain?
no_cv <- trainControl(method = "none")
set.seed(42)
tree_full <- train(
Sales ~ .,
data = test_df,
method = "rpart",
trControl = no_cv,
tuneGrid = data.frame(cp = 0)
)
rpart.plot(tree_full$finalModel, type = 2, fallen.leaves = TRUE)
pred.full <- predict(tree_full, newdata = test_df)
print(mean((pred.full - test_df$Sales)^2))## [1] 3.573815- Use cross-validation in order to determine the optimal level of tree complexity. Does pruning the tree improve the test MSE?
cv <- trainControl(method = "cv", number = 10)
set.seed(42)
cv_tree <- train(
Sales ~ .,
data = train_df,
method = "rpart",
trControl = cv,
tuneLength = 10
)## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo,
## : There were missing values in resampled performance measures.rpart.plot(cv_tree$finalModel, type = 2, fallen.leaves = TRUE)
pred.pruned <- predict(cv_tree, newdata = test_df)
print(mean((pred.pruned- test_df$Sales)^2))## [1] 4.109234- Use the bagging approach in order to analyze this data. What test MSE do you obtain? Use the feature_importance_ values to determine which variables are most important.
set.seed(1)
bag_fit <- train(
Sales ~ .,
data = train_df,
method = "treebag",
trControl = cv,
importance = TRUE
)
pred_bag <- predict(bag_fit, newdata = test_df)
mse_bag <- mean((pred_bag - test_df$Sales)^2)
print(mse_bag)## [1] 3.125146varImp(bag_fit)## treebag variable importance
##
## Overall
## Price 100.00000
## Age 82.66471
## CompPrice 74.29577
## Advertising 68.50321
## Income 53.53561
## Population 30.16667
## Education 24.54921
## ShelveLocMedium 21.34672
## USYes 7.96713
## ShelveLocGood 0.09579
## UrbanYes 0.00000plot(varImp(bag_fit))
- Use random forests to analyze this data. What test MSE do you obtain? Use the feature_importance_ values to determine which variables are most important. Describe the effect of m, the number of variables considered at each split, on the error rate obtained.
set.seed(42)
rf_fit <- train(
Sales ~ .,
data = train_df,
method = "rf",
trControl = cv,
importance = TRUE,
tuneGrid = expand.grid(mtry = 1:10)
)
print(rf_fit$bestTune$mtry)## [1] 10pred_rf <- predict(rf_fit, newdata = test_df)
mse_rf <- mean((pred_rf - test_df$Sales)^2)
print(mse_rf)## [1] 2.608174varImp(rf_fit)## rf variable importance
##
## Overall
## ShelveLocGood 100.000
## Price 86.130
## CompPrice 47.692
## ShelveLocMedium 40.086
## Advertising 37.785
## Age 30.136
## Income 12.934
## Education 11.463
## USYes 10.729
## UrbanYes 6.415
## Population 0.000plot(varImp(rf_fit))
- Now analyze the data using BART, and report your results
library(BART)## Warning: package 'BART' was built under R version 4.3.3## Loading required package: nlme## Warning: package 'nlme' was built under R version 4.3.3##
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##
## clusterx_train <- train_df[, -1]
y_train <- train_df$Sales
x_test <- test_df[, -1]
y_test <- test_df$Sales
set.seed(1)
bart_fit <- gbart(x_train, y_train, x.test = x_test)## *****Calling gbart: type=1
## *****Data:
## data:n,p,np: 321, 14, 79
## y1,yn: 1.954953, 2.164953
## x1,x[n*p]: 138.000000, 1.000000
## xp1,xp[np*p]: 111.000000, 0.000000
## *****Number of Trees: 200
## *****Number of Cut Points: 70 ... 1
## *****burn,nd,thin: 100,1000,1
## *****Prior:beta,alpha,tau,nu,lambda,offset: 2,0.95,0.287616,3,0.187591,7.54505
## *****sigma: 0.981343
## *****w (weights): 1.000000 ... 1.000000
## *****Dirichlet:sparse,theta,omega,a,b,rho,augment: 0,0,1,0.5,1,14,0
## *****printevery: 100
##
## MCMC
## done 0 (out of 1100)
## done 100 (out of 1100)
## done 200 (out of 1100)
## done 300 (out of 1100)
## done 400 (out of 1100)
## done 500 (out of 1100)
## done 600 (out of 1100)
## done 700 (out of 1100)
## done 800 (out of 1100)
## done 900 (out of 1100)
## done 1000 (out of 1100)
## time: 3s
## trcnt,tecnt: 1000,1000pred_bart <- bart_fit$yhat.test.mean
mse_bart <- mean((pred_bart - y_test)^2)
print(mse_bart)## [1] 1.687287Problem 9
This problem involves the OJ data set which is part of the ISLP package.
- Create a training set containing a random sample of 800 observations, and a test set containing the remaining observations.
data(OJ)
head(OJ)## Purchase WeekofPurchase StoreID PriceCH PriceMM DiscCH DiscMM SpecialCH
## 1 CH 237 1 1.75 1.99 0.00 0.0 0
## 2 CH 239 1 1.75 1.99 0.00 0.3 0
## 3 CH 245 1 1.86 2.09 0.17 0.0 0
## 4 MM 227 1 1.69 1.69 0.00 0.0 0
## 5 CH 228 7 1.69 1.69 0.00 0.0 0
## 6 CH 230 7 1.69 1.99 0.00 0.0 0
## SpecialMM LoyalCH SalePriceMM SalePriceCH PriceDiff Store7 PctDiscMM
## 1 0 0.500000 1.99 1.75 0.24 No 0.000000
## 2 1 0.600000 1.69 1.75 -0.06 No 0.150754
## 3 0 0.680000 2.09 1.69 0.40 No 0.000000
## 4 0 0.400000 1.69 1.69 0.00 No 0.000000
## 5 0 0.956535 1.69 1.69 0.00 Yes 0.000000
## 6 1 0.965228 1.99 1.69 0.30 Yes 0.000000
## PctDiscCH ListPriceDiff STORE
## 1 0.000000 0.24 1
## 2 0.000000 0.24 1
## 3 0.091398 0.23 1
## 4 0.000000 0.00 1
## 5 0.000000 0.00 0
## 6 0.000000 0.30 0set.seed(42)
train_idx.oj <- sample(1:nrow(OJ), 800)
OJ_train <- OJ[train_idx.oj, ]
OJ_test <- OJ[-train_idx.oj, ]- Fit a tree to the training data, with Purchase as the response and the other variables as predictors. What is the training error rate?
ctrl <- trainControl(method = "none")
tree_fit <- train(Purchase ~ ., data = OJ_train,
method = "rpart",
trControl = ctrl,
tuneGrid = data.frame(cp = 0.001))
train_pred <- predict(tree_fit, OJ_train)
train_err <- mean(train_pred != OJ_train$Purchase)
print(train_err)## [1] 0.1325- Create a plot of the tree, and interpret the results. How many terminal nodes does the tree have?
rpart.plot(tree_fit$finalModel, extra = 104, fallen.leaves = TRUE)
n_terminal <- sum(tree_fit$finalModel$frame$var == "<leaf>")
print(n_terminal)## [1] 18- Use the export_tree() function to produce a text summary of the fitted tree. Pick one of the terminal nodes, and interpret the information displayed.
print(tree_fit$finalModel) ## n= 800
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 800 308 CH (0.61500000 0.38500000)
## 2) LoyalCH>=0.48285 515 84 CH (0.83689320 0.16310680)
## 4) LoyalCH>=0.705699 313 19 CH (0.93929712 0.06070288)
## 8) PriceDiff>=-0.39 298 11 CH (0.96308725 0.03691275) *
## 9) PriceDiff< -0.39 15 7 MM (0.46666667 0.53333333) *
## 5) LoyalCH< 0.705699 202 65 CH (0.67821782 0.32178218)
## 10) ListPriceDiff>=0.235 120 22 CH (0.81666667 0.18333333)
## 20) PriceDiff>=0.31 40 2 CH (0.95000000 0.05000000) *
## 21) PriceDiff< 0.31 80 20 CH (0.75000000 0.25000000)
## 42) StoreID>=2.5 56 9 CH (0.83928571 0.16071429) *
## 43) StoreID< 2.5 24 11 CH (0.54166667 0.45833333)
## 86) LoyalCH< 0.635456 17 6 CH (0.64705882 0.35294118) *
## 87) LoyalCH>=0.635456 7 2 MM (0.28571429 0.71428571) *
## 11) ListPriceDiff< 0.235 82 39 MM (0.47560976 0.52439024)
## 22) PctDiscCH>=0.052007 12 1 CH (0.91666667 0.08333333) *
## 23) PctDiscCH< 0.052007 70 28 MM (0.40000000 0.60000000)
## 46) LoyalCH>=0.5945395 41 20 MM (0.48780488 0.51219512)
## 92) DiscMM< 0.3 27 11 CH (0.59259259 0.40740741)
## 184) ListPriceDiff>=0.115 8 1 CH (0.87500000 0.12500000) *
## 185) ListPriceDiff< 0.115 19 9 MM (0.47368421 0.52631579) *
## 93) DiscMM>=0.3 14 4 MM (0.28571429 0.71428571) *
## 47) LoyalCH< 0.5945395 29 8 MM (0.27586207 0.72413793)
## 94) StoreID>=2.5 13 6 CH (0.53846154 0.46153846) *
## 95) StoreID< 2.5 16 1 MM (0.06250000 0.93750000) *
## 3) LoyalCH< 0.48285 285 61 MM (0.21403509 0.78596491)
## 6) LoyalCH>=0.2761415 127 45 MM (0.35433071 0.64566929)
## 12) SalePriceMM>=2.04 51 24 CH (0.52941176 0.47058824)
## 24) PriceMM< 2.155 20 6 CH (0.70000000 0.30000000) *
## 25) PriceMM>=2.155 31 13 MM (0.41935484 0.58064516)
## 50) LoyalCH>=0.424473 7 2 CH (0.71428571 0.28571429) *
## 51) LoyalCH< 0.424473 24 8 MM (0.33333333 0.66666667) *
## 13) SalePriceMM< 2.04 76 18 MM (0.23684211 0.76315789)
## 26) SpecialCH>=0.5 13 5 CH (0.61538462 0.38461538) *
## 27) SpecialCH< 0.5 63 10 MM (0.15873016 0.84126984) *
## 7) LoyalCH< 0.2761415 158 16 MM (0.10126582 0.89873418) *summary(tree_fit$finalModel) ## Call:
## (function (formula, data, weights, subset, na.action = na.rpart,
## method, model = FALSE, x = FALSE, y = TRUE, parms, control,
## cost, ...)
## {
## Call <- match.call()
## if (is.data.frame(model)) {
## m <- model
## model <- FALSE
## }
## else {
## indx <- match(c("formula", "data", "weights", "subset"),
## names(Call), nomatch = 0)
## if (indx[1] == 0)
## stop("a 'formula' argument is required")
## temp <- Call[c(1, indx)]
## temp$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)) {
## if (!all(names(control) %in% names(controls)))
## stop("unkown named elements in 'control'")
## controls <- do.call(rpart.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(245, 257, 239, 246,
## 264, 229, 272, 270, 255, 262, 260, 227, 229, 269, 259, 264, 274,
## 252, 231, 276, 276, 231, 254, 233, 274, 253, 240, 264, 276, 256,
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## 278, 245, 276, 263, 276, 233, 257, 248, 271, 231, 241, 246, 264,
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## 277, 258, 275, 271, 272, 260, 252, 268, 258, 232, 269, 277, 256,
## 239, 271, 248, 259, 274, 245, 236, 253, 275, 238, 257, 246, 277,
## 228, 232, 267, 266, 273, 249, 259, 265, 229, 265, 258, 256, 254,
## 257, 242, 259, 275, 255, 233, 255, 259, 244, 265, 261, 260, 251,
## 256, 229, 275, 262, 237, 255, 243, 260, 263, 244, 247, 270, 233,
## 243, 271, 274, 251, 256, 237, 237, 236, 237, 264, 242, 275, 238,
## 232, 247, 269, 243, 269, 262, 257, 274, 270, 274, 267, 266, 277,
## 241, 261, 228, 269, 229, 265, 274, 259, 275, 261, 241, 238, 274,
## 268, 235, 229, 241, 255, 233, 269, 238, 266, 262, 267, 230, 273,
## 270, 235, 262, 234, 227, 244, 259, 234, 235, 240, 274, 227, 236,
## 267, 272, 274, 273, 237, 235, 273, 234, 254, 278, 267, 260, 259,
## 265, 240, 229, 238, 246, 231, 230, 240, 255, 242, 240, 235, 277,
## 248, 230, 257, 271, 236, 231, 228, 239, 276, 267, 245, 239, 239,
## 275, 243, 259, 254, 269, 237, 269, 230, 267, 236, 259, 241, 272,
## 278, 254, 243, 252, 268, 258, 243, 270, 260, 237, 232, 278, 231,
## 262, 243, 256, 240, 275, 269, 264, 235, 270, 263, 232, 246, 263,
## 274, 240, 230, 264, 236, 236, 233, 253, 263, 275, 235, 246, 264,
## 269, 257, 261, 233, 264, 274, 263, 242, 271, 275, 264, 261, 269,
## 236, 259, 255, 271, 231, 230, 257, 258, 228, 266, 257, 276, 262,
## 247, 228, 256, 262, 239, 278, 267, 247, 230, 259, 266, 273, 260,
## 260, 258, 261, 272, 265, 275, 261, 267, 251, 235, 263, 277, 230,
## 232, 254, 228, 247, 229, 267, 265, 273, 274, 277, 231, 236, 275,
## 238, 274, 229, 234, 239, 227, 236, 269, 268, 252, 275, 258, 275,
## 241, 257, 256, 267, 236, 272, 253, 258, 277, 228, 227, 233, 274,
## 259, 247, 237, 269, 261, 272, 278, 272, 274, 251, 262, 267, 260,
## 244, 231, 266, 242, 275, 251, 242, 251, 258, 271, 239, 270, 275,
## 240, 237, 240, 270, 228, 274, 273, 241, 278, 245, 273, 266, 237,
## 243, 264, 269, 242, 234, 277, 272, 257, 251, 255, 266, 251, 277,
## 268, 256, 256, 251, 240, 269, 271, 234, 260, 253, 276, 270, 229,
## 275, 249, 242, 270, 248, 230, 257, 268, 246, 233, 252, 253, 237,
## 274, 267, 262, 238, 271, 266, 253, 258, 233, 236, 231, 265, 276,
## 276, 274, 267), c(2, 3, 3, 4, 7, 4, 4, 1, 7, 7, 7, 4, 7, 7, 1,
## 3, 7, 7, 2, 7, 2, 4, 7, 7, 4, 1, 3, 7, 3, 2, 2, 7, 2, 7, 2, 7,
## 1, 2, 1, 3, 2, 4, 3, 2, 1, 2, 3, 2, 2, 4, 2, 4, 1, 2, 3, 2, 4,
## 7, 4, 4, 7, 3, 1, 7, 2, 2, 4, 2, 4, 2, 3, 7, 4, 2, 3, 7, 1, 2,
## 2, 2, 4, 1, 4, 4, 1, 3, 3, 2, 4, 3, 7, 7, 1, 2, 1, 3, 4, 1, 3,
## 7, 7, 1, 3, 3, 1, 3, 7, 2, 2, 7, 7, 2, 4, 2, 7, 7, 1, 7, 7, 4,
## 3, 3, 7, 7, 1, 1, 1, 1, 7, 1, 4, 1, 7, 3, 1, 2, 1, 7, 3, 7, 1,
## 2, 7, 2, 1, 3, 1, 2, 1, 2, 3, 7, 4, 7, 3, 2, 1, 4, 7, 7, 4, 7,
## 2, 7, 7, 1, 3, 7, 4, 3, 3, 3, 2, 3, 1, 7, 1, 7, 2, 2, 4, 4, 2,
## 2, 7, 3, 2, 7, 2, 1, 2, 3, 2, 3, 3, 7, 7, 7, 4, 4, 7, 7, 4, 3,
## 4, 3, 2, 2, 4, 1, 3, 2, 7, 7, 1, 1, 3, 2, 7, 2, 7, 2, 7, 3, 4,
## 4, 1, 1, 7, 1, 7, 7, 7, 7, 3, 3, 3, 7, 3, 2, 7, 7, 2, 4, 7, 1,
## 1, 2, 7, 3, 7, 3, 7, 4, 7, 3, 4, 7, 4, 4, 7, 7, 2, 1, 3, 7, 1,
## 3, 2, 3, 7, 3, 4, 2, 7, 7, 3, 2, 1, 7, 3, 7, 7, 7, 7, 2, 2, 7,
## 7, 7, 3, 3, 1, 1, 7, 3, 7, 2, 2, 7, 4, 2, 2, 7, 2, 3, 2, 2, 1,
## 7, 7, 1, 3, 4, 3, 4, 1, 3, 2, 3, 4, 2, 7, 7, 4, 3, 4, 7, 3, 4,
## 2, 2, 7, 1, 3, 1, 2, 7, 7, 2, 7, 3, 7, 7, 1, 1, 7, 4, 2, 7, 1,
## 7, 1, 7, 4, 7, 3, 4, 2, 3, 7, 4, 3, 7, 7, 7, 3, 7, 4, 2, 7, 7,
## 7, 7, 3, 2, 3, 1, 3, 3, 1, 4, 7, 2, 2, 4, 1, 1, 2, 7, 7, 1, 3,
## 7, 3, 1, 1, 2, 7, 4, 4, 3, 7, 4, 7, 4, 2, 4, 2, 4, 3, 7, 1, 1,
## 7, 1, 7, 7, 7, 4, 2, 2, 7, 1, 3, 2, 3, 1, 3, 7, 7, 7, 7, 1, 3,
## 7, 7, 7, 1, 3, 2, 1, 7, 2, 4, 4, 3, 7, 7, 7, 7, 2, 3, 3, 7, 1,
## 2, 2, 7, 4, 4, 4, 7, 1, 3, 2, 1, 2, 4, 3, 2, 1, 2, 1, 3, 1, 7,
## 1, 2, 1, 7, 7, 7, 7, 7, 2, 2, 1, 2, 7, 2, 7, 7, 1, 7, 1, 3, 2,
## 7, 3, 4, 2, 7, 7, 7, 7, 3, 1, 4, 3, 2, 4, 7, 3, 1, 4, 4, 2, 7,
## 2, 4, 7, 3, 7, 7, 2, 7, 2, 7, 2, 2, 3, 2, 2, 7, 2, 2, 7, 2, 2,
## 2, 2, 2, 7, 7, 4, 3, 1, 3, 7, 2, 3, 3, 4, 2, 7, 1, 2, 7, 4, 3,
## 2, 3, 1, 1, 7, 7, 1, 2, 7, 7, 2, 3, 7, 3, 4, 2, 7, 2, 3, 2, 7,
## 4, 4, 3, 2, 3, 7, 2, 2, 1, 7, 3, 7, 4, 2, 7, 7, 7, 1, 3, 4, 3,
## 3, 7, 7, 7, 3, 7, 2, 2, 2, 7, 3, 4, 2, 7, 7, 7, 3, 2, 7, 7, 3,
## 2, 2, 7, 4, 7, 3, 4, 7, 3, 3, 4, 7, 7, 3, 4, 7, 2, 1, 2, 7, 1,
## 7, 7, 2, 2, 4, 2, 4, 1, 2, 7, 4, 7, 7, 7, 7, 7, 1, 1, 3, 2, 7,
## 7, 2, 2, 2, 3, 3, 3, 1, 2, 3, 7, 7, 7, 4, 3, 4, 2, 7, 7, 1, 2,
## 7, 1, 3, 2, 1, 7, 1, 7, 7, 2, 7, 4, 7, 7, 7, 2, 1, 2, 7, 7, 3,
## 1, 7, 1, 1, 2, 4, 4, 4, 2, 3, 7, 3, 2, 7, 3, 3, 3, 2, 4, 7, 3,
## 1, 7, 2, 1, 3, 7, 7, 2, 7, 1, 1, 7, 2, 1, 2, 7, 1, 3, 3, 1, 3,
## 4, 7, 7, 3, 4, 7, 1, 7, 7, 4, 2, 4, 4, 4, 4, 7, 1, 1, 7, 2, 3,
## 2, 1, 2, 3, 1, 1, 7, 3, 3, 7, 2, 7, 4, 7, 4, 7, 2, 7, 1, 7, 3,
## 7, 2, 1, 4, 2, 4, 7, 3), c(1.89, 1.99, 1.79, 1.99, 1.86, 1.79,
## 1.99, 1.86, 1.86, 1.86, 1.86, 1.79, 1.69, 1.86, 1.76, 1.99, 1.86,
## 1.86, 1.69, 1.99, 1.99, 1.79, 1.86, 1.75, 1.99, 1.76, 1.79, 1.86,
## 2.09, 1.89, 1.86, 1.86, 1.86, 1.75, 1.86, 1.86, 1.69, 1.69, 1.69,
## 1.79, 1.89, 1.79, 2.09, 1.96, 1.75, 1.75, 1.99, 1.89, 1.86, 1.99,
## 1.86, 1.79, 1.99, 1.86, 1.79, 1.69, 2.09, 2.06, 1.79, 2.09, 1.86,
## 1.99, 1.69, 1.86, 1.86, 1.75, 1.99, 1.86, 1.99, 1.86, 1.99, 1.86,
## 1.99, 1.86, 2.09, 1.86, 1.86, 1.69, 1.69, 1.86, 1.79, 1.69, 1.99,
## 1.99, 1.69, 1.99, 1.99, 1.89, 1.99, 1.99, 1.75, 1.86, 1.75, 1.69,
## 1.69, 1.79, 1.99, 1.76, 1.99, 1.86, 1.75, 1.69, 1.99, 1.99, 1.75,
## 1.99, 1.86, 1.86, 1.99, 1.99, 1.86, 1.89, 1.79, 1.75, 1.69, 1.86,
## 1.76, 1.86, 1.86, 2.09, 1.99, 1.79, 1.75, 1.86, 1.76, 1.86, 1.69,
## 1.75, 1.69, 1.96, 1.99, 1.75, 1.86, 1.99, 1.76, 1.69, 1.86, 1.86,
## 1.79, 1.75, 1.86, 1.89, 1.86, 1.86, 1.86, 2.09, 1.69, 1.89, 1.86,
## 1.69, 2.09, 1.86, 1.99, 1.86, 1.79, 1.86, 1.86, 1.79, 1.86, 1.86,
## 1.79, 1.86, 1.69, 1.86, 1.86, 1.86, 1.79, 1.86, 1.99, 1.99, 1.99,
## 1.79, 1.86, 1.79, 1.76, 1.69, 1.76, 1.99, 1.69, 1.86, 1.99, 1.99,
## 1.86, 1.86, 1.99, 1.99, 1.89, 1.86, 1.99, 1.86, 1.89, 1.99, 1.89,
## 1.79, 1.99, 1.86, 1.86, 1.86, 1.99, 1.99, 1.86, 1.86, 2.09, 1.99,
## 1.99, 1.79, 1.86, 1.86, 1.99, 1.86, 1.79, 1.75, 2.06, 1.86, 1.75,
## 1.76, 1.99, 1.89, 1.86, 1.69, 1.75, 1.86, 1.86, 1.99, 1.99, 1.79,
## 1.76, 1.96, 1.75, 1.86, 1.99, 1.75, 1.99, 1.86, 2.09, 1.99, 1.99,
## 1.69, 1.99, 1.86, 1.69, 1.86, 1.96, 1.99, 1.86, 1.76, 1.69, 1.75,
## 1.69, 1.79, 1.86, 1.79, 1.75, 1.79, 1.86, 1.99, 1.99, 1.86, 2.09,
## 1.79, 1.86, 1.86, 1.99, 1.69, 1.79, 1.86, 1.86, 2.09, 1.86, 1.99,
## 1.86, 1.99, 1.99, 1.89, 1.86, 1.86, 1.79, 1.99, 1.69, 1.86, 2.09,
## 1.69, 1.75, 1.86, 1.86, 1.89, 1.99, 1.86, 1.86, 1.99, 1.79, 1.79,
## 1.96, 1.86, 1.99, 1.79, 1.86, 1.86, 1.86, 1.69, 1.99, 1.86, 1.75,
## 1.86, 1.89, 1.79, 1.96, 1.86, 1.69, 1.86, 1.86, 1.86, 1.99, 1.79,
## 1.99, 1.79, 1.76, 1.99, 1.96, 1.99, 1.79, 1.75, 1.75, 1.69, 1.99,
## 1.79, 1.99, 1.86, 1.79, 1.99, 1.86, 1.69, 1.69, 1.96, 1.99, 1.86,
## 1.69, 1.86, 1.86, 1.99, 1.86, 1.99, 1.86, 1.86, 1.86, 1.99, 1.86,
## 2.09, 1.86, 1.75, 1.86, 1.86, 1.86, 1.86, 1.99, 1.86, 1.99, 1.99,
## 1.89, 1.79, 1.86, 1.79, 2.09, 1.86, 1.86, 1.86, 1.79, 1.86, 2.09,
## 1.89, 1.99, 1.86, 1.99, 1.75, 1.99, 1.89, 1.99, 1.69, 1.79, 1.99,
## 1.76, 1.99, 1.86, 1.86, 1.75, 1.99, 1.69, 1.76, 1.86, 1.86, 1.86,
## 1.69, 1.99, 1.86, 2.09, 1.76, 1.96, 1.86, 1.86, 1.99, 1.99, 1.99,
## 1.86, 1.79, 1.86, 2.09, 1.89, 1.79, 1.86, 1.99, 1.99, 1.86, 1.86,
## 1.75, 1.86, 1.96, 1.75, 1.86, 1.86, 2.09, 1.69, 1.69, 1.86, 1.86,
## 1.99, 1.89, 1.99, 1.76, 1.79, 1.86, 1.86, 1.86, 1.86, 1.76, 1.99,
## 1.86, 1.99, 1.86, 1.69, 1.99, 1.86, 1.86, 1.86, 1.86, 1.99, 1.99,
## 1.99, 1.69, 1.99, 1.86, 1.75, 1.89, 1.99, 1.99, 1.86, 1.86, 1.89,
## 1.86, 1.75, 1.99, 1.99, 1.99, 1.86, 1.76, 1.79, 1.75, 1.75, 1.75,
## 1.99, 1.99, 1.96, 1.75, 1.69, 1.86, 1.99, 1.86, 1.86, 1.76, 1.86,
## 1.96, 1.86, 1.86, 1.86, 1.86, 1.99, 1.75, 1.86, 1.69, 1.86, 1.69,
## 1.86, 1.86, 1.86, 1.96, 1.86, 1.86, 1.79, 1.96, 1.86, 1.79, 1.79,
## 1.75, 1.86, 1.75, 1.86, 1.75, 1.99, 1.76, 1.99, 1.79, 1.86, 1.99,
## 1.75, 1.99, 1.69, 1.79, 1.99, 1.86, 1.75, 1.69, 1.79, 1.86, 1.79,
## 1.75, 1.86, 1.86, 1.86, 1.86, 1.75, 1.69, 1.86, 1.79, 1.89, 1.99,
## 1.86, 1.86, 1.86, 1.86, 1.75, 1.69, 1.75, 1.89, 1.69, 1.69, 1.86,
## 1.99, 1.99, 1.75, 1.79, 1.99, 1.89, 1.79, 1.99, 1.99, 1.75, 1.69,
## 1.69, 1.75, 1.99, 1.99, 1.99, 1.75, 1.79, 1.96, 1.86, 1.86, 1.86,
## 1.86, 1.75, 1.86, 1.69, 1.86, 1.79, 1.86, 1.79, 1.99, 1.99, 1.86,
## 1.86, 1.99, 1.86, 1.86, 1.99, 1.99, 1.99, 1.75, 1.79, 2.06, 1.69,
## 1.86, 1.86, 1.86, 1.79, 1.99, 1.99, 1.86, 1.75, 1.86, 1.86, 1.69,
## 1.99, 1.99, 1.99, 1.79, 1.69, 1.86, 1.75, 1.79, 1.75, 1.89, 1.86,
## 1.96, 1.75, 1.99, 1.99, 1.86, 1.86, 1.86, 1.75, 1.99, 1.96, 1.86,
## 1.86, 1.99, 1.96, 1.86, 1.86, 1.99, 1.75, 1.99, 1.99, 1.86, 1.79,
## 1.79, 1.99, 1.86, 1.69, 1.99, 1.99, 1.99, 1.86, 1.86, 1.69, 1.86,
## 1.76, 1.79, 2.06, 1.86, 1.89, 1.79, 1.86, 1.99, 1.86, 1.86, 1.86,
## 1.99, 1.86, 1.86, 1.86, 1.99, 1.86, 1.86, 1.76, 1.79, 1.86, 1.99,
## 1.69, 1.69, 1.89, 1.69, 1.99, 1.79, 1.99, 1.76, 1.86, 1.99, 1.99,
## 1.69, 1.75, 2.09, 1.79, 1.99, 1.69, 1.75, 1.79, 1.69, 1.75, 1.86,
## 1.86, 1.99, 1.96, 1.76, 1.99, 1.86, 1.86, 1.86, 1.86, 1.75, 1.99,
## 1.86, 1.86, 1.99, 1.69, 1.69, 1.69, 1.86, 1.86, 1.99, 1.75, 1.86,
## 1.76, 1.86, 1.99, 1.99, 1.99, 1.99, 1.86, 1.99, 1.86, 1.99, 1.69,
## 1.86, 1.99, 2.09, 1.99, 1.75, 1.99, 1.86, 1.99, 1.75, 1.86, 1.96,
## 1.75, 1.79, 1.86, 1.86, 1.69, 1.86, 1.86, 1.86, 2.06, 1.89, 1.86,
## 1.86, 1.75, 1.86, 1.99, 1.99, 1.86, 1.79, 2.09, 1.86, 1.86, 1.99,
## 1.99, 1.86, 1.76, 1.99, 1.86, 1.99, 1.89, 1.99, 1.79, 1.99, 1.99,
## 1.75, 1.76, 1.76, 1.99, 1.86, 1.79, 1.96, 1.86, 1.75, 1.99, 1.86,
## 1.69, 1.86, 1.99, 1.99, 1.75, 1.89, 1.86, 1.79, 1.86, 1.99, 1.86,
## 1.75, 1.86, 1.86, 1.86, 1.99, 1.75, 1.75, 1.69, 1.99, 1.99, 2.09,
## 1.86, 1.99), c(2.09, 2.29, 2.23, 2.23, 2.13, 1.79, 2.09, 2.18,
## 2.18, 2.13, 2.13, 1.79, 1.69, 2.13, 1.99, 2.09, 2.13, 2.09, 1.69,
## 2.13, 2.18, 1.79, 2.18, 1.99, 2.09, 2.09, 2.23, 2.13, 2.09, 2.18,
## 2.18, 2.13, 2.18, 1.99, 2.18, 2.13, 1.69, 1.69, 1.99, 2.09, 2.09,
## 1.79, 2.09, 2.18, 1.99, 1.99, 2.23, 2.09, 2.18, 2.09, 2.18, 2.09,
## 2.13, 2.18, 2.23, 1.99, 2.09, 2.13, 1.79, 2.09, 2.13, 2.09, 1.69,
## 2.13, 2.18, 1.99, 2.09, 2.18, 2.09, 2.18, 2.09, 2.09, 2.09, 2.18,
## 2.09, 2.09, 2.09, 1.99, 1.69, 2.18, 2.09, 1.99, 2.23, 2.29, 1.99,
## 2.09, 2.09, 2.18, 2.29, 2.23, 1.99, 2.13, 1.99, 1.69, 1.99, 2.09,
## 2.09, 2.18, 2.23, 2.13, 1.99, 1.99, 2.09, 2.09, 1.99, 2.09, 2.13,
## 2.18, 2.18, 2.13, 2.13, 2.09, 1.79, 1.99, 1.99, 2.13, 2.18, 2.09,
## 2.13, 2.09, 2.23, 1.79, 1.99, 2.09, 1.99, 2.18, 1.99, 1.99, 1.99,
## 2.13, 2.23, 1.99, 2.13, 2.09, 1.99, 1.69, 1.99, 2.09, 2.09, 1.99,
## 1.99, 2.09, 2.13, 2.18, 1.99, 2.09, 1.99, 2.09, 2.09, 1.69, 2.09,
## 2.13, 2.09, 2.13, 1.79, 2.18, 1.99, 1.79, 2.13, 2.09, 1.79, 2.13,
## 1.69, 2.13, 2.13, 2.09, 2.09, 2.13, 2.09, 2.23, 2.29, 1.79, 2.18,
## 2.09, 1.99, 1.69, 2.18, 2.13, 1.69, 2.09, 2.09, 2.23, 2.18, 2.18,
## 2.13, 2.29, 2.18, 2.09, 2.18, 1.99, 2.09, 2.23, 2.09, 1.79, 2.23,
## 2.09, 2.18, 2.18, 2.23, 2.09, 2.18, 2.13, 2.09, 2.09, 2.09, 2.09,
## 2.18, 2.18, 2.09, 2.18, 2.23, 1.99, 2.13, 2.13, 1.99, 1.99, 2.23,
## 2.09, 2.09, 1.69, 1.99, 2.18, 2.13, 2.29, 2.29, 1.79, 1.99, 2.13,
## 1.99, 2.18, 2.13, 1.99, 2.13, 2.13, 2.09, 2.09, 2.09, 1.69, 2.23,
## 2.18, 1.69, 2.13, 2.18, 2.09, 2.18, 2.09, 1.69, 1.99, 1.69, 2.23,
## 2.13, 2.09, 1.99, 1.79, 2.18, 2.09, 2.29, 2.09, 2.09, 1.79, 2.18,
## 2.18, 2.18, 1.99, 1.79, 2.13, 1.99, 2.09, 2.18, 2.09, 2.09, 2.09,
## 2.09, 2.09, 2.13, 2.13, 2.23, 2.18, 1.99, 2.13, 2.09, 1.99, 1.99,
## 2.18, 2.13, 2.18, 2.18, 2.13, 2.13, 2.13, 1.79, 1.79, 2.13, 2.18,
## 2.13, 2.23, 2.13, 2.18, 2.09, 1.69, 2.23, 2.18, 1.99, 2.18, 2.09,
## 1.79, 2.18, 2.18, 1.99, 2.18, 2.13, 2.18, 2.29, 2.23, 2.29, 2.23,
## 2.18, 2.23, 2.18, 2.09, 2.09, 1.99, 1.99, 1.99, 2.23, 2.09, 2.23,
## 2.18, 2.23, 2.09, 2.18, 1.69, 1.99, 2.13, 2.09, 2.09, 1.69, 2.13,
## 2.13, 2.18, 2.18, 2.09, 2.13, 2.18, 1.99, 2.13, 2.13, 2.09, 2.18,
## 1.99, 2.18, 2.13, 2.18, 2.09, 2.09, 2.18, 2.23, 2.09, 2.09, 2.09,
## 2.18, 2.09, 2.09, 2.09, 2.13, 2.13, 1.79, 2.09, 2.09, 2.09, 2.13,
## 2.13, 2.13, 1.99, 2.29, 2.09, 2.09, 1.69, 2.23, 2.23, 1.99, 2.29,
## 2.13, 2.18, 1.99, 2.29, 1.69, 2.09, 2.18, 2.13, 2.09, 1.99, 2.23,
## 2.13, 2.09, 2.18, 2.13, 2.18, 2.13, 2.09, 2.23, 2.09, 2.18, 2.09,
## 2.13, 2.09, 2.18, 2.23, 2.18, 2.23, 2.29, 2.13, 2.09, 1.99, 2.09,
## 2.13, 1.99, 2.18, 2.09, 2.09, 1.69, 1.69, 2.13, 1.99, 2.09, 2.09,
## 2.29, 1.99, 1.79, 2.13, 2.18, 2.18, 2.18, 2.18, 2.23, 2.18, 2.13,
## 2.18, 1.99, 2.29, 2.18, 2.09, 2.13, 2.18, 2.09, 2.23, 2.29, 1.69,
## 2.13, 2.13, 1.99, 2.18, 2.23, 2.09, 2.13, 2.09, 2.09, 2.18, 1.99,
## 2.23, 2.09, 2.09, 2.09, 2.18, 2.09, 1.99, 1.99, 1.99, 2.09, 2.23,
## 2.18, 1.99, 1.69, 2.09, 2.09, 1.99, 2.13, 1.99, 2.18, 2.13, 2.13,
## 2.13, 2.13, 2.13, 2.13, 1.99, 2.18, 1.69, 2.18, 1.69, 2.18, 2.13,
## 2.18, 2.13, 2.13, 1.99, 2.09, 2.18, 2.13, 2.09, 1.79, 1.99, 2.18,
## 1.99, 2.13, 1.99, 2.09, 1.99, 2.09, 1.79, 2.18, 2.09, 1.99, 2.09,
## 1.99, 1.79, 2.23, 2.18, 1.99, 1.99, 2.23, 2.13, 1.79, 1.99, 2.13,
## 2.18, 2.13, 2.18, 1.99, 1.99, 2.18, 2.09, 2.09, 2.18, 2.13, 2.18,
## 2.18, 2.13, 1.99, 1.69, 1.99, 2.09, 1.69, 1.99, 2.09, 2.29, 2.23,
## 1.99, 2.09, 2.13, 2.09, 1.79, 2.29, 2.09, 1.99, 1.99, 1.69, 1.99,
## 2.13, 2.09, 2.23, 1.99, 2.23, 2.13, 1.99, 2.18, 2.18, 2.18, 1.99,
## 2.13, 1.99, 2.18, 2.09, 2.18, 2.23, 2.09, 2.18, 2.18, 2.09, 2.23,
## 2.18, 2.18, 2.23, 2.09, 2.09, 1.99, 2.09, 2.13, 1.69, 2.18, 1.99,
## 2.18, 2.23, 2.13, 2.09, 2.18, 1.99, 2.13, 2.13, 1.99, 2.23, 2.09,
## 2.09, 2.23, 1.99, 2.13, 1.99, 2.09, 1.99, 2.09, 2.18, 2.18, 1.99,
## 2.23, 2.09, 2.18, 2.18, 2.13, 1.99, 2.09, 2.18, 2.13, 2.09, 2.09,
## 2.18, 2.18, 2.13, 2.09, 1.99, 2.29, 2.29, 2.13, 1.79, 1.79, 2.29,
## 2.18, 1.69, 2.09, 2.29, 2.13, 2.18, 2.09, 1.69, 2.18, 1.99, 2.09,
## 2.13, 2.18, 2.09, 1.79, 2.18, 2.09, 2.18, 2.18, 2.13, 2.29, 2.13,
## 2.13, 2.13, 2.13, 2.13, 1.99, 2.09, 2.09, 2.18, 2.13, 1.99, 1.69,
## 2.09, 1.69, 2.23, 1.79, 2.09, 1.99, 2.18, 2.09, 2.13, 1.99, 1.99,
## 2.09, 2.09, 2.09, 1.69, 1.99, 2.09, 1.69, 1.99, 2.13, 1.99, 2.23,
## 2.18, 2.18, 2.13, 1.99, 2.18, 2.18, 2.18, 1.99, 2.09, 2.09, 2.18,
## 2.13, 1.69, 1.69, 1.69, 2.13, 2.18, 2.23, 1.99, 2.13, 1.99, 2.18,
## 2.18, 2.09, 2.09, 2.23, 2.18, 2.09, 2.13, 2.23, 1.69, 2.13, 2.23,
## 2.09, 2.23, 1.99, 2.23, 2.18, 2.09, 1.99, 2.13, 2.18, 1.99, 2.09,
## 2.09, 2.13, 1.69, 2.13, 2.18, 1.99, 2.13, 2.09, 2.18, 2.18, 1.99,
## 1.99, 2.09, 2.09, 1.99, 2.09, 2.09, 2.13, 2.18, 2.23, 2.29, 2.13,
## 2.09, 2.13, 2.13, 2.29, 2.18, 2.23, 2.23, 2.09, 2.09, 1.99, 1.99,
## 2.09, 2.13, 2.18, 1.79, 2.18, 2.09, 1.99, 2.09, 2.09, 1.69, 2.18,
## 2.09, 2.23, 1.99, 2.09, 2.09, 2.09, 2.13, 2.09, 2.13, 1.99, 2.13,
## 1.99, 2.09, 2.29, 1.99, 1.99, 1.69, 2.09, 2.18, 2.09, 2.13, 2.09
## ), c(0, 0, 0, 0, 0.37, 0, 0, 0, 0, 0, 0, 0, 0, 0.27, 0, 0.1,
## 0.47, 0.1, 0.3, 0, 0, 0, 0, 0, 0, 0, 0, 0.37, 0.2, 0.13, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.2, 0, 0, 0, 0, 0, 0, 0.1, 0,
## 0, 0.24, 0, 0, 0, 0.2, 0, 0, 0, 0.37, 0, 0, 0.47, 0, 0, 0.1,
## 0, 0.1, 0, 0, 0, 0, 0, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0.1, 0.13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.27, 0, 0, 0, 0.1,
## 0, 0.1, 0.37, 0, 0, 0.5, 0.37, 0, 0, 0, 0, 0.27, 0, 0, 0, 0.2,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.37, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0.27, 0, 0, 0.2, 0, 0.13, 0, 0, 0.2, 0.47, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0.37, 0, 0.17, 0, 0, 0.1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0.1, 0, 0, 0, 0.5, 0, 0.13, 0, 0, 0, 0, 0,
## 0.13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.2, 0, 0, 0, 0, 0, 0.1, 0,
## 0, 0.16, 0, 0.47, 0, 0, 0, 0.13, 0, 0, 0, 0, 0.27, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0.47, 0, 0.1, 0, 0, 0, 0, 0, 0.37, 0, 0, 0,
## 0, 0, 0, 0, 0, 0.37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0.2, 0, 0.1, 0, 0.1, 0, 0.13, 0, 0.37, 0, 0, 0, 0, 0.2,
## 0, 0, 0, 0.47, 0.13, 0, 0.47, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.37, 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, 0.1, 0, 0,
## 0, 0.27, 0, 0, 0, 0.47, 0, 0, 0.24, 0.27, 0.2, 0, 0, 0, 0.37,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.2, 0, 0, 0.37, 0, 0, 0.2, 0,
## 0, 0.27, 0, 0, 0, 0, 0.1, 0.3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0.37, 0.1, 0, 0, 0.37, 0.2, 0, 0, 0, 0, 0, 0, 0.1, 0, 0, 0.27,
## 0.2, 0.13, 0, 0, 0, 0, 0.47, 0.17, 0, 0.1, 0, 0, 0, 0, 0.2, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0.37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0.37, 0, 0, 0, 0, 0, 0, 0, 0, 0.13, 0, 0, 0.27, 0, 0, 0, 0,
## 0, 0.1, 0, 0.1, 0, 0, 0, 0, 0, 0.1, 0, 0, 0, 0, 0, 0.1, 0, 0.27,
## 0, 0, 0, 0.27, 0.47, 0, 0.37, 0.5, 0, 0, 0, 0, 0, 0, 0.47, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.27, 0, 0.1, 0, 0.1, 0, 0,
## 0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.47, 0, 0, 0, 0, 0.47, 0, 0,
## 0, 0, 0, 0.13, 0, 0, 0, 0, 0.37, 0, 0, 0, 0, 0.3, 0, 0, 0, 0,
## 0, 0, 0.5, 0, 0, 0, 0.1, 0, 0, 0, 0, 0, 0.1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0.27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.1, 0,
## 0, 0, 0, 0.3, 0, 0, 0, 0, 0, 0.1, 0, 0, 0.27, 0.27, 0, 0, 0,
## 0, 0, 0, 0.37, 0, 0, 0, 0.13, 0, 0, 0, 0, 0.1, 0, 0, 0, 0, 0.1,
## 0, 0.27, 0, 0.1, 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, 0.1, 0, 0, 0, 0, 0, 0,
## 0.37, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0.13, 0, 0, 0, 0.1, 0, 0,
## 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.27, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0.1, 0, 0.5, 0, 0, 0, 0.47, 0, 0, 0, 0.27, 0,
## 0, 0, 0, 0, 0, 0, 0.1, 0, 0, 0.3, 0.37, 0, 0, 0, 0.16, 0, 0,
## 0.1, 0, 0.27, 0, 0, 0, 0, 0.27, 0, 0.47, 0, 0, 0, 0, 0, 0, 0,
## 0, 0.1, 0.1, 0, 0, 0.2, 0, 0, 0, 0, 0.37, 0, 0.5, 0, 0, 0.13,
## 0, 0, 0.1, 0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0.16, 0.1, 0, 0, 0, 0.1,
## 0, 0, 0.13, 0.1, 0, 0.47, 0.1, 0, 0, 0, 0, 0.1, 0, 0, 0, 0.3,
## 0.1, 0, 0.2, 0.47, 0.1), c(0, 0.4, 0, 0, 0, 0, 0.4, 0, 0, 0,
## 0.24, 0, 0.2, 0, 0.2, 0, 0.54, 0, 0, 0.54, 0, 0, 0, 0.4, 0.4,
## 0, 0, 0, 0.4, 0, 0, 0.54, 0, 0.4, 0, 0.24, 0, 0, 0, 0, 0, 0,
## 0.4, 0.8, 0, 0.3, 0, 0, 0, 0, 0, 0, 0, 0.4, 0, 0, 0.4, 0, 0,
## 0.4, 0, 0, 0.2, 0.54, 0.7, 0, 0, 0, 0, 0.06, 0.4, 0.2, 0, 0,
## 0.4, 0.2, 0, 0, 0, 0.06, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.4, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0.4, 0, 0.4, 0, 0, 0, 0, 0.06, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.4, 0, 0, 0.4, 0, 0.4, 0, 0, 0.3,
## 0, 0.74, 0, 0.3, 0, 0, 0.4, 0, 0.1, 0.2, 0, 0.4, 0.8, 0, 0, 0.06,
## 0.1, 0, 0, 0, 0, 0, 0.4, 0.54, 0, 0, 0, 0.6, 0.3, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.6, 0, 0.4, 0.2, 0, 0.54, 0,
## 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0.1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0.3, 0, 0.54, 0.3, 0.2,
## 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0.74, 0.4, 0, 0.54, 0.4, 0.54,
## 0.54, 0.4, 0.4, 0.4, 0.2, 0, 0.06, 0, 0, 0.8, 0.4, 0, 0, 0, 0,
## 0.2, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0.3,
## 0, 0, 0, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.4, 0, 0.54,
## 0, 0, 0.54, 0.24, 0, 0, 0, 0.74, 0, 0.54, 0, 0, 0, 0, 0.2, 0,
## 0, 0, 0, 0, 0, 0.8, 0.7, 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0.8,
## 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0.7, 0, 0.4, 0.74, 0, 0, 0,
## 0.24, 0, 0, 0, 0, 0.54, 0, 0.8, 0, 0, 0.4, 0.06, 0.4, 0, 0, 0,
## 0.2, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0.2, 0, 0, 0, 0.2, 0, 0, 0.54,
## 0, 0.54, 0.4, 0.4, 0, 0.4, 0.2, 0, 0, 0.4, 0, 0.24, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0.4, 0, 0.74, 0.06, 0, 0, 0, 0, 0, 0,
## 0, 0.4, 0, 0, 0.06, 0, 0, 0.54, 0, 0, 0, 0.74, 0.4, 0, 0, 0.4,
## 0, 0, 0, 0.1, 0.4, 0, 0, 0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0.54, 0,
## 0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0.2, 0.54, 0, 0.4, 0, 0, 0, 0, 0,
## 0, 0, 0.4, 0, 0.4, 0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0.8, 0, 0, 0,
## 0, 0.8, 0, 0.4, 0, 0.74, 0, 0.54, 0, 0, 0, 0.3, 0, 0, 0, 0.2,
## 0, 0.54, 0, 0.74, 0.24, 0.3, 0, 0.8, 0, 0, 0, 0.3, 0, 0.4, 0,
## 0.4, 0, 0.4, 0, 0, 0.06, 0, 0.4, 0, 0, 0, 0, 0.4, 0.4, 0, 0,
## 0.54, 0, 0.4, 0, 0.06, 0.54, 0.06, 0.4, 0, 0.06, 0, 0, 0, 0,
## 0.7, 0.4, 0, 0.3, 0, 0, 0, 0, 0, 0, 0, 0, 0.3, 0, 0, 0, 0, 0.4,
## 0.4, 0, 0, 0, 0.3, 0.54, 0, 0, 0.3, 0, 0.74, 0.8, 0, 0, 0, 0,
## 0, 0, 0.4, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0.6, 0.8, 0, 0, 0.54, 0, 0, 0.4, 0, 0, 0, 0, 0, 0.4, 0, 0,
## 0, 0.4, 0, 0.4, 0, 0, 0.8, 0.4, 0, 0, 0, 0, 0.24, 0.4, 0, 0.8,
## 0, 0, 0.4, 0.8, 0, 0.24, 0, 0.4, 0, 0, 0, 0, 0, 0.4, 0, 0, 0,
## 0.4, 0.54, 0.6, 0, 0, 0, 0.4, 0, 0, 0.4, 0, 0, 0.4, 0, 0, 0.7,
## 0.24, 0, 0.24, 0, 0, 0.54, 0.24, 0.2, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0.1, 0.06, 0.4, 0, 0, 0.4, 0.4, 0, 0.4, 0, 0.4, 0, 0,
## 0, 0, 0.2, 0, 0.8, 0, 0.54, 0.3, 0, 0, 0.4, 0.4, 0.4, 0, 0, 0,
## 0, 0, 0, 0.54, 0, 0, 0, 0, 0, 0, 0, 0.4, 0.4, 0, 0.6, 0, 0.24,
## 0, 0, 0, 0, 0.4, 0, 0.3, 0, 0, 0.4, 0.3, 0, 0.8, 0.3, 0, 0, 0,
## 0, 0.54, 0, 0.3, 0, 0, 0, 0, 0.4, 0.8, 0, 0, 0.3, 0, 0.4, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.4, 0.4, 0.2, 0, 0.54, 0,
## 0, 0.8, 0, 0.3, 0, 0, 0.2, 0, 0, 0, 0.4, 0, 0, 0, 0.54, 0, 0,
## 0, 0, 0.1, 0, 0, 0.4, 0, 0.2, 0, 0, 0.4, 0.54, 0), c(0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 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, 1, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0,
## 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0,
## 0, 0, 1, 0, 0, 0, 0, 1, 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, 0, 0, 1, 0, 0, 1,
## 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 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, 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, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1,
## 0, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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## 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
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## 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 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, 0, 1, 1,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0,
## 0, 0, 0, 0, 0, 1, 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, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0,
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## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
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## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 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, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1,
## 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0),
## c(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 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, 1, 0, 1, 0, 1, 0, 0, 1, 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,
## 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0,
## 0, 1, 0, 0, 0, 0, 0, 1, 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, 0, 0, 0, 0,
## 0, 1, 0, 1, 1, 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, 0, 0, 1, 0,
## 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 1, 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, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0,
## 0, 0, 1, 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, 1, 1, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 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, 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, 1, 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, 1, 0, 0, 0, 0,
## 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1,
## 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0,
## 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0,
## 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0,
## 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1,
## 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 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, 1, 0, 1, 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, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 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), c(0.5, 0.6, 0.813222, 0.886992, 0.7952, 0.4, 0.988741,
## 0.914616, 0.421938, 0.916114, 0.955332, 0.5, 0.6, 0.89327,
## 0.972512, 0.6, 0.803392, 0.587822, 0.4672, 0.112583, 0.729346,
## 0.6, 0.52, 0.5, 0.99987, 0.459072, 0.6928, 0.4928, 1.1e-05,
## 0.022751, 0.616, 0.965027, 0.3072, 0.084671, 0.912618, 0.769835,
## 0.5, 0.5, 0.857394, 0.007206, 0.891914, 0.920961, 0.983112,
## 0.68, 0.456, 0.916114, 0.4, 0.89609, 0.32, 0.65184, 0.256,
## 0.744, 0.082564, 0.68, 0.868928, 0.136315, 0.32, 0.7952,
## 0.32, 0.4, 0.97592, 0.083886, 0.4, 0.592251, 0.456, 0.60576,
## 0.932891, 0.4, 0.767142, 0.6, 0.253687, 0.444965, 0.6, 0.005964,
## 0.000203, 0.256, 0.5, 0.83616, 0.584, 0.274861, 0.5, 0.586313,
## 0.995388, 0.834969, 0.7952, 0.001209, 5.3e-05, 0.5, 0.891202,
## 0.002361, 0.5, 0.866588, 0.350822, 0.256, 0.868928, 0.540992,
## 0.104858, 0.6672, 0.946798, 0.7952, 0.4, 0.4048, 0.6, 0.958768,
## 0.52, 8.3e-05, 0.946313, 0.471378, 0.32, 0.384, 0.895142,
## 0.228587, 0.949415, 0.5648, 0.481092, 0.987671, 0.584, 0.953271,
## 0.83616, 0.850971, 0.002361, 0.26624, 0.926986, 0.77574,
## 0.4, 0.931693, 0.5, 0.721472, 0.67616, 0.863685, 0.6, 0.65184,
## 0.2048, 0.94846, 0.616, 0.108486, 0.416, 0.52, 0.16384, 0.5,
## 0.4048, 0.2048, 0.96083, 0.000317, 0.988291, 0.986489, 0.83616,
## 0.68, 0.73524, 0.170394, 0.5328, 0.5, 0.999033, 0.993688,
## 0.5648, 0.4, 0.556206, 0.936769, 0.999683, 0.5, 0.833801,
## 0.52, 0.744, 0.850578, 0.95705, 0.83764, 0.7952, 0.68, 0.97801,
## 0.880462, 0.001209, 0.4, 0.009319, 0.009007, 0.053687, 0.4,
## 0.70816, 0.98534, 0.211886, 0.256, 0.92458, 0.83616, 0.018201,
## 0.32, 0.4, 0.396608, 0.68, 0.996311, 0.148096, 0.829332,
## 0.069431, 0.916114, 0.18287, 0.027488, 0.803392, 0.061203,
## 0.32, 0.5, 0.994235, 0.606319, 0.938797, 0.895142, 0.999947,
## 0.343577, 0.930369, 0.45184, 0.283886, 0.979164, 0.944296,
## 0.671172, 0.249713, 0.4, 0.6, 0.5, 0.6, 0.6, 0.831116, 0.610093,
## 0.850578, 0.4, 0.6, 0.201954, 0.990885, 0.001511, 0.5, 0.6672,
## 0.787008, 0.664742, 0.5, 0.464858, 0.999896, 0.985757, 0.99495,
## 0.670435, 0.752851, 0.973612, 0.067109, 0.68, 0.002951, 0.6928,
## 0.584, 0.981704, 0.661682, 0.95705, 0.6672, 0.32384, 0.32,
## 0.895142, 0.95705, 0.7952, 0.68, 0.017592, 0.4, 0.4, 0.131072,
## 0.038103, 0.7952, 0.813222, 0.96564, 0.83616, 0.856474, 0.670258,
## 0.988272, 0.916114, 0.027488, 0.97801, 0.777178, 0.561472,
## 0.6, 0.000495, 0.32, 6.6e-05, 0.999226, 0.757438, 0.895142,
## 0.985363, 0.670149, 0.972512, 0.4, 0.984589, 0.995388, 0.65184,
## 0.069793, 0.4, 0.629047, 0.844761, 0.5, 0.5, 0.951037, 0.3328,
## 0.16384, 0.256, 0.44576, 0.956283, 0.589079, 0.005765, 0.890948,
## 0.331072, 0.746313, 0.68, 0.68, 0.36384, 0.267737, 0.358548,
## 0.5, 0.02199, 0.744, 0.959305, 0.619072, 0.744, 0.932891,
## 0.982408, 0.074419, 0.77928, 0.001511, 0.893632, 0.32, 0.007206,
## 0.175911, 0.000162, 0.867041, 0.16384, 0.766528, 0.256, 0.94554,
## 0.299008, 0.5, 0.16384, 0.788895, 0.95705, 0.94466, 0.2048,
## 0.6, 0.740314, 0.967015, 0.946313, 0.165373, 0.712294, 0.588044,
## 0.645286, 0.68, 0.000396, 0.972021, 0.787008, 0.277422, 0.103205,
## 0.675392, 0.819719, 0.985493, 0.09563, 0.433472, 0.9699,
## 0.930094, 0.2048, 0.912962, 0.5, 0.256, 0.616, 0.744, 0.131072,
## 0.923496, 0.97801, 0.273285, 0.6, 0.4, 0.427109, 0.04295,
## 0.992794, 0.855775, 0.281092, 0.48, 0.932891, 0.616, 0.4,
## 0.875808, 0.870112, 3.4e-05, 0.32, 0.6, 0.384, 0.791543,
## 0.640368, 0.916114, 0.5, 0.171351, 0.997639, 0.4, 0.821742,
## 0.955728, 0.999604, 0.5, 0.48, 0.416, 0.83616, 0.450072,
## 0.68, 0.161258, 0.944076, 0.6, 0.998791, 0.793712, 0.90437,
## 0.864003, 0.4, 0.95705, 0.97801, 0.55046, 0.4, 0.788394,
## 0.5, 0.000619, 0.985926, 0.68, 0.695258, 0.5, 0.68, 0.792742,
## 0.863685, 0.256, 0.994235, 0.5, 0.5, 0.983956, 0.4, 2.2e-05,
## 0.916872, 0.936414, 0.833234, 0.48, 0.4, 0.83616, 0.5, 0.6672,
## 0.083886, 0.6, 0.744, 0.972512, 0.03917, 0.4352, 0.199771,
## 0.6672, 0.4, 0.868928, 0.973955, 0.63616, 0.6, 0.32, 0.5,
## 0.703238, 0.971413, 0.32, 0.035549, 0.005765, 0.935575, 0.813222,
## 0.251966, 0.68, 0.981866, 0.52384, 0.32, 0.999797, 0.965145,
## 0.7952, 0.908732, 0.5, 0.4, 0.346778, 0.484608, 0.946313,
## 0.5, 0.231401, 0.16384, 0.4352, 0.66905, 0.174028, 0.314957,
## 0.868928, 0.68, 0.900647, 0.731794, 0.990137, 0.411886, 0.787008,
## 0.916114, 0.961385, 0.932891, 0.83616, 0.5, 0.977333, 0.16384,
## 0.786665, 0.766528, 0.744, 0.477037, 0.48, 0.3648, 0.719675,
## 0.977093, 0.980736, 0.616, 0.792251, 0.5, 0.6, 0.628114,
## 0.992506, 0.2048, 0.52, 0.5, 0.972512, 0.131072, 0.427008,
## 0.699827, 0.885915, 0.964583, 0.256, 0.5, 0.914906, 0.949131,
## 0.977746, 0.32, 0.985926, 0.6, 0.053687, 0.6, 0.990633, 0.95526,
## 0.6, 0.577102, 0.544, 0.109052, 0.556608, 0.02199, 0.805951,
## 0.716229, 0.932891, 0.7952, 0.4, 0.6, 0.83616, 0.169509,
## 0.744, 0.48, 0.5, 0.544, 0.988606, 0.6, 0.45184, 0.224526,
## 0.5, 0.32, 0.16384, 0.283886, 0.000774, 0.4, 0.68, 0.6352,
## 0.32, 0.70816, 0.416, 0.813714, 0.004612, 0.044668, 0.017592,
## 0.571886, 0.6, 0.868928, 0.73376, 0.96564, 0.086789, 0.52,
## 0.5648, 0.32, 0.077677, 0.930207, 0.63616, 0.559861, 0.6,
## 0.766528, 0.834194, 0.3072, 0.4, 0.908143, 0.990993, 0.27335,
## 0.695749, 0.214189, 0.104858, 0.946313, 0.135607, 0.271919,
## 0.4, 0.619686, 0.014074, 0.736348, 0.946313, 0.983331, 0.561993,
## 0.6, 0.852695, 0.52, 0.5, 0.932891, 0.978889, 0.011259, 0.132298,
## 0.968664, 0.507899, 0.649594, 0.5, 0.6, 0.007455, 0.000254,
## 0.982197, 0.708928, 0.999381, 0.32, 0.6, 0.32, 0.524608,
## 0.000254, 0.392858, 0.868928, 0.988741, 0.4, 0.210886, 0.584,
## 0.588965, 0.6, 0.908732, 0.047628, 0.998111, 0.863685, 0.895142,
## 0.868928, 0.787504, 0.890948, 0.535142, 0.000619, 0.998489,
## 0.992708, 0.4, 0.331072, 0.48, 0.829606, 0.6, 0.137081, 0.982408,
## 0.003817, 0.68, 0.52, 0.68, 0.804349, 0.70816, 0.427109,
## 0.941212, 0.830003, 0.952969, 0.916114, 0.59424, 0.6, 0.964266,
## 0.491072, 0.355972, 0.181687, 0.445279, 0.131072, 0.96564,
## 0.68, 0.930825, 0.32, 0.003689, 0.03436, 0.000104, 0.3072,
## 0.264858, 1.7e-05, 0.97801, 0.68, 0.4, 0.774649, 0.14535,
## 0.990993, 0.7952, 0.6, 0.982408, 0.4, 0.5, 0.95705, 0.2048,
## 0.874171, 0.981675, 0.73376, 0.140729, 0.5, 0.7952, 0.90437,
## 0.484979, 0.4, 0.951731, 0.6, 0.256, 0.988741, 0.6, 0.6,
## 0.105838, 0.219889, 0.014561, 0.32, 0.5, 0.972512, 0.384,
## 0.945354, 0.826781, 0.999838, 0.718311, 0.5, 0.256, 0.6,
## 0.895142, 0.75424, 0.212992, 0.616, 0.131072, 1.4e-05, 0.544,
## 0.895142, 0.48, 0.68, 0.6, 0.280658, 0.987165, 0.4, 0.5,
## 0.256, 0.941588, 0.939664, 0.4, 0.97801, 0.580928, 0.179621,
## 0.4, 0.79705, 0.971367, 0.004771, 0.740928, 0.32, 0.68, 0.5,
## 0.24576, 0.256, 0.384, 0.21868, 0.885179, 0.5, 0.895142,
## 0.52, 0.456, 0.994005, 0.946313, 0.73438, 0.4, 0.997049,
## 0.5, 0.874783, 0.985926, 0.5, 0.815868, 0.5, 0.2048, 0.000396,
## 0.4, 0.168709, 0.933497, 0.131072, 4.3e-05, 0.931925, 0.544,
## 0.198186, 0.003054, 0.5, 0.2048, 0.868928, 0.83616, 0.9741,
## 0.314286, 0.843479, 0.97713, 0.055835, 0.99211, 0.68, 0.96564,
## 0.919469, 0.384874, 0.868928, 0.5, 0.4, 0.18512, 0.992794,
## 0.96564, 0.00013), c(2.09, 1.89, 2.23, 2.23, 2.13, 1.79,
## 1.69, 2.18, 2.18, 2.13, 1.89, 1.79, 1.49, 2.13, 1.79, 2.09,
## 1.59, 2.09, 1.69, 1.59, 2.18, 1.79, 2.18, 1.59, 1.69, 2.09,
## 2.23, 2.13, 1.69, 2.18, 2.18, 1.59, 2.18, 1.59, 2.18, 1.89,
## 1.69, 1.69, 1.99, 2.09, 2.09, 1.79, 1.69, 1.38, 1.99, 1.69,
## 2.23, 2.09, 2.18, 2.09, 2.18, 2.09, 2.13, 1.78, 2.23, 1.99,
## 1.69, 2.13, 1.79, 1.69, 2.13, 2.09, 1.49, 1.59, 1.48, 1.99,
## 2.09, 2.18, 2.09, 2.12, 1.69, 1.89, 2.09, 2.18, 1.69, 1.89,
## 2.09, 1.99, 1.69, 2.12, 2.09, 1.99, 2.23, 2.29, 1.99, 2.09,
## 2.09, 2.18, 2.29, 2.23, 1.59, 2.13, 1.99, 1.69, 1.99, 2.09,
## 2.09, 2.18, 2.23, 2.13, 1.59, 1.99, 1.69, 2.09, 1.99, 2.09,
## 2.13, 2.12, 2.18, 2.13, 2.13, 2.09, 1.79, 1.99, 1.99, 2.13,
## 2.18, 2.09, 2.13, 1.69, 2.23, 1.79, 1.59, 2.09, 1.59, 2.18,
## 1.99, 1.69, 1.99, 1.39, 2.23, 1.69, 2.13, 2.09, 1.59, 1.69,
## 1.89, 1.89, 2.09, 1.59, 1.19, 2.09, 2.13, 2.12, 1.89, 2.09,
## 1.99, 2.09, 2.09, 1.69, 1.69, 1.59, 2.09, 2.13, 1.79, 1.58,
## 1.69, 1.79, 2.13, 2.09, 1.79, 2.13, 1.69, 2.13, 2.13, 2.09,
## 2.09, 2.13, 2.09, 2.23, 2.29, 1.79, 1.58, 2.09, 1.59, 1.49,
## 2.18, 1.59, 1.69, 2.09, 2.09, 2.23, 2.18, 1.78, 2.13, 2.29,
## 2.18, 2.09, 2.18, 1.89, 2.09, 2.23, 2.09, 1.79, 2.23, 2.09,
## 2.18, 2.18, 2.23, 2.09, 2.18, 2.13, 2.09, 1.69, 2.09, 2.09,
## 2.18, 2.18, 2.09, 2.18, 2.23, 1.69, 2.13, 1.59, 1.69, 1.79,
## 2.23, 2.09, 2.09, 1.69, 1.59, 2.18, 2.13, 2.29, 2.29, 1.79,
## 1.99, 1.39, 1.59, 2.18, 1.59, 1.59, 1.59, 1.59, 1.69, 1.69,
## 1.69, 1.49, 2.23, 2.12, 1.69, 2.13, 1.38, 1.69, 2.18, 2.09,
## 1.69, 1.99, 1.49, 2.23, 2.13, 2.09, 1.59, 1.79, 2.18, 2.09,
## 2.29, 2.09, 1.69, 1.79, 2.18, 2.18, 2.18, 1.99, 1.79, 2.13,
## 1.69, 2.09, 2.18, 2.09, 1.89, 2.09, 2.09, 2.09, 2.13, 2.13,
## 2.23, 2.18, 1.99, 2.13, 2.09, 1.99, 1.59, 2.18, 1.59, 2.18,
## 2.18, 1.59, 1.89, 2.13, 1.79, 1.79, 1.39, 2.18, 1.59, 2.23,
## 2.13, 2.18, 2.09, 1.49, 2.23, 2.18, 1.99, 2.18, 2.09, 1.79,
## 1.38, 1.48, 1.99, 2.18, 2.13, 2.18, 1.89, 2.23, 2.29, 2.23,
## 2.18, 2.23, 1.38, 2.09, 2.09, 1.99, 1.59, 1.99, 2.23, 2.09,
## 2.23, 2.18, 2.23, 2.09, 1.48, 1.69, 1.59, 1.39, 2.09, 2.09,
## 1.69, 1.89, 2.13, 2.18, 2.18, 2.09, 1.59, 2.18, 1.19, 2.13,
## 2.13, 1.69, 2.12, 1.59, 2.18, 2.13, 2.18, 1.89, 2.09, 2.18,
## 2.23, 1.69, 2.09, 2.09, 2.18, 2.09, 2.09, 1.89, 2.13, 2.13,
## 1.79, 1.89, 2.09, 2.09, 1.59, 2.13, 1.59, 1.59, 1.89, 2.09,
## 1.69, 1.49, 2.23, 2.23, 1.59, 2.29, 1.89, 2.18, 1.99, 2.29,
## 1.69, 2.09, 2.18, 2.13, 2.09, 1.99, 2.23, 2.13, 1.69, 2.18,
## 1.39, 2.12, 2.13, 2.09, 2.23, 2.09, 2.18, 2.09, 2.13, 1.69,
## 2.18, 2.23, 2.12, 2.23, 2.29, 1.59, 2.09, 1.99, 2.09, 1.39,
## 1.59, 2.18, 2.09, 1.69, 1.69, 1.69, 2.13, 1.89, 1.69, 2.09,
## 2.29, 1.89, 1.79, 2.13, 2.18, 2.18, 2.18, 2.18, 2.23, 2.18,
## 1.59, 2.18, 1.99, 2.29, 1.78, 2.09, 2.13, 2.18, 2.09, 2.23,
## 2.29, 1.49, 1.59, 2.13, 1.59, 2.18, 2.23, 2.09, 2.13, 2.09,
## 2.09, 2.18, 1.59, 2.23, 1.69, 1.69, 2.09, 2.18, 2.09, 1.99,
## 1.99, 1.99, 2.09, 2.23, 1.38, 1.99, 1.69, 2.09, 2.09, 1.19,
## 2.13, 1.59, 2.18, 1.39, 2.13, 1.59, 2.13, 2.13, 2.13, 1.69,
## 2.18, 1.69, 2.18, 1.49, 2.18, 1.59, 2.18, 1.39, 1.89, 1.69,
## 2.09, 1.38, 2.13, 2.09, 1.79, 1.69, 2.18, 1.59, 2.13, 1.59,
## 2.09, 1.59, 2.09, 1.79, 2.12, 2.09, 1.59, 2.09, 1.99, 1.79,
## 2.23, 1.78, 1.59, 1.99, 2.23, 1.59, 1.79, 1.59, 2.13, 2.12,
## 1.59, 2.12, 1.59, 1.99, 2.12, 2.09, 2.09, 2.18, 2.13, 1.48,
## 1.78, 2.13, 1.69, 1.69, 1.99, 2.09, 1.69, 1.99, 2.09, 2.29,
## 2.23, 1.69, 2.09, 2.13, 2.09, 1.79, 1.89, 1.69, 1.99, 1.99,
## 1.69, 1.69, 1.59, 2.09, 2.23, 1.69, 2.23, 1.39, 1.19, 2.18,
## 2.18, 2.18, 1.99, 2.13, 1.99, 1.78, 2.09, 2.18, 2.23, 1.69,
## 2.18, 2.18, 2.09, 2.23, 2.18, 2.18, 2.23, 2.09, 2.09, 1.99,
## 2.09, 2.13, 1.69, 1.58, 1.19, 2.18, 2.23, 1.59, 2.09, 2.18,
## 1.59, 2.13, 2.13, 1.99, 2.23, 2.09, 1.69, 2.23, 1.99, 2.13,
## 1.59, 2.09, 1.59, 2.09, 2.18, 1.38, 1.59, 2.23, 2.09, 2.18,
## 2.18, 1.89, 1.59, 2.09, 1.38, 2.13, 2.09, 1.69, 1.38, 2.18,
## 1.89, 2.09, 1.59, 2.29, 2.29, 2.13, 1.79, 1.79, 1.89, 2.18,
## 1.69, 2.09, 1.89, 1.59, 1.58, 2.09, 1.69, 2.18, 1.59, 2.09,
## 2.13, 1.78, 2.09, 1.79, 1.78, 2.09, 2.18, 1.48, 1.89, 2.29,
## 1.89, 2.13, 2.13, 1.59, 1.89, 1.79, 2.09, 2.09, 2.18, 2.13,
## 1.99, 1.69, 2.09, 1.69, 2.23, 1.79, 2.09, 1.89, 2.12, 1.69,
## 2.13, 1.99, 1.59, 1.69, 2.09, 1.69, 1.69, 1.59, 2.09, 1.69,
## 1.99, 2.13, 1.79, 2.23, 1.38, 2.18, 1.59, 1.69, 2.18, 2.18,
## 1.78, 1.59, 1.69, 2.09, 2.18, 2.13, 1.69, 1.69, 1.69, 1.59,
## 2.18, 2.23, 1.99, 2.13, 1.99, 2.18, 2.18, 1.69, 1.69, 2.23,
## 1.58, 2.09, 1.89, 2.23, 1.69, 2.13, 2.23, 1.69, 2.23, 1.69,
## 2.23, 2.18, 1.69, 1.69, 2.13, 1.38, 1.69, 2.09, 2.09, 2.13,
## 1.69, 1.59, 2.18, 1.69, 2.13, 2.09, 2.18, 2.18, 1.59, 1.19,
## 2.09, 2.09, 1.69, 2.09, 1.69, 2.13, 2.18, 2.23, 2.29, 2.13,
## 2.09, 2.13, 2.13, 2.29, 2.18, 2.23, 2.23, 2.09, 1.69, 1.59,
## 1.79, 2.09, 1.59, 2.18, 1.79, 1.38, 2.09, 1.69, 2.09, 2.09,
## 1.49, 2.18, 2.09, 2.23, 1.59, 2.09, 2.09, 2.09, 1.59, 2.09,
## 2.13, 1.99, 2.13, 1.89, 2.09, 2.29, 1.59, 1.99, 1.49, 2.09,
## 2.18, 1.69, 1.59, 2.09), c(1.89, 1.99, 1.79, 1.99, 1.49,
## 1.79, 1.99, 1.86, 1.86, 1.86, 1.86, 1.79, 1.69, 1.59, 1.76,
## 1.89, 1.39, 1.76, 1.39, 1.99, 1.99, 1.79, 1.86, 1.75, 1.99,
## 1.76, 1.79, 1.49, 1.89, 1.76, 1.86, 1.86, 1.86, 1.75, 1.86,
## 1.86, 1.69, 1.69, 1.69, 1.79, 1.89, 1.79, 1.89, 1.96, 1.75,
## 1.75, 1.99, 1.89, 1.86, 1.89, 1.86, 1.79, 1.75, 1.86, 1.79,
## 1.69, 1.89, 2.06, 1.79, 2.09, 1.49, 1.99, 1.69, 1.39, 1.86,
## 1.75, 1.89, 1.86, 1.89, 1.86, 1.99, 1.86, 1.99, 1.86, 1.89,
## 1.86, 1.86, 1.69, 1.69, 1.86, 1.79, 1.69, 1.99, 1.99, 1.69,
## 1.99, 1.89, 1.76, 1.99, 1.99, 1.75, 1.86, 1.75, 1.69, 1.69,
## 1.79, 1.99, 1.76, 1.99, 1.59, 1.75, 1.69, 1.99, 1.89, 1.75,
## 1.89, 1.49, 1.86, 1.99, 1.49, 1.49, 1.89, 1.79, 1.75, 1.69,
## 1.59, 1.76, 1.86, 1.86, 1.89, 1.99, 1.79, 1.75, 1.86, 1.76,
## 1.86, 1.69, 1.75, 1.69, 1.96, 1.99, 1.75, 1.49, 1.99, 1.76,
## 1.69, 1.86, 1.86, 1.79, 1.75, 1.86, 1.89, 1.59, 1.86, 1.86,
## 1.89, 1.69, 1.76, 1.86, 1.69, 1.89, 1.39, 1.99, 1.86, 1.79,
## 1.86, 1.86, 1.79, 1.86, 1.86, 1.79, 1.86, 1.69, 1.49, 1.86,
## 1.69, 1.79, 1.86, 1.89, 1.99, 1.99, 1.79, 1.86, 1.79, 1.76,
## 1.69, 1.76, 1.99, 1.69, 1.86, 1.89, 1.99, 1.86, 1.86, 1.49,
## 1.99, 1.76, 1.86, 1.99, 1.86, 1.89, 1.99, 1.76, 1.79, 1.99,
## 1.86, 1.86, 1.86, 1.99, 1.99, 1.86, 1.86, 1.89, 1.99, 1.99,
## 1.79, 1.86, 1.86, 1.89, 1.86, 1.79, 1.59, 2.06, 1.39, 1.75,
## 1.76, 1.99, 1.76, 1.86, 1.69, 1.75, 1.86, 1.59, 1.99, 1.99,
## 1.79, 1.76, 1.96, 1.75, 1.86, 1.99, 1.75, 1.99, 1.39, 2.09,
## 1.89, 1.99, 1.69, 1.99, 1.86, 1.69, 1.49, 1.96, 1.99, 1.86,
## 1.76, 1.69, 1.75, 1.69, 1.79, 1.49, 1.79, 1.75, 1.79, 1.86,
## 1.99, 1.99, 1.86, 2.09, 1.79, 1.86, 1.86, 1.99, 1.69, 1.79,
## 1.86, 1.86, 1.89, 1.86, 1.89, 1.86, 1.89, 1.99, 1.76, 1.86,
## 1.49, 1.79, 1.99, 1.69, 1.86, 1.89, 1.69, 1.75, 1.86, 1.39,
## 1.76, 1.99, 1.39, 1.86, 1.49, 1.79, 1.79, 1.96, 1.86, 1.99,
## 1.79, 1.86, 1.86, 1.86, 1.69, 1.99, 1.86, 1.75, 1.86, 1.89,
## 1.79, 1.96, 1.86, 1.69, 1.86, 1.49, 1.86, 1.99, 1.79, 1.99,
## 1.79, 1.76, 1.99, 1.96, 1.89, 1.79, 1.75, 1.75, 1.69, 1.99,
## 1.79, 1.99, 1.86, 1.79, 1.89, 1.86, 1.69, 1.69, 1.96, 1.89,
## 1.86, 1.69, 1.86, 1.59, 1.99, 1.86, 1.99, 1.39, 1.86, 1.86,
## 1.75, 1.59, 1.89, 1.86, 1.75, 1.86, 1.49, 1.86, 1.86, 1.99,
## 1.86, 1.99, 1.99, 1.89, 1.79, 1.86, 1.79, 1.89, 1.86, 1.86,
## 1.49, 1.79, 1.86, 1.89, 1.89, 1.99, 1.59, 1.99, 1.75, 1.99,
## 1.89, 1.89, 1.39, 1.79, 1.99, 1.76, 1.99, 1.86, 1.86, 1.75,
## 1.99, 1.69, 1.76, 1.86, 1.49, 1.76, 1.69, 1.99, 1.49, 1.89,
## 1.76, 1.96, 1.86, 1.86, 1.99, 1.99, 1.89, 1.86, 1.79, 1.59,
## 1.89, 1.76, 1.79, 1.86, 1.99, 1.99, 1.39, 1.69, 1.75, 1.76,
## 1.96, 1.75, 1.86, 1.86, 1.89, 1.69, 1.69, 1.86, 1.86, 1.99,
## 1.89, 1.99, 1.76, 1.79, 1.49, 1.86, 1.86, 1.86, 1.76, 1.99,
## 1.86, 1.99, 1.86, 1.69, 1.99, 1.86, 1.86, 1.49, 1.86, 1.99,
## 1.99, 1.99, 1.69, 1.99, 1.86, 1.75, 1.76, 1.99, 1.99, 1.59,
## 1.86, 1.89, 1.86, 1.75, 1.99, 1.89, 1.99, 1.76, 1.76, 1.79,
## 1.75, 1.75, 1.75, 1.89, 1.99, 1.96, 1.75, 1.69, 1.86, 1.89,
## 1.86, 1.59, 1.76, 1.86, 1.96, 1.59, 1.39, 1.86, 1.49, 1.49,
## 1.75, 1.86, 1.69, 1.86, 1.69, 1.86, 1.39, 1.86, 1.96, 1.86,
## 1.86, 1.79, 1.96, 1.86, 1.79, 1.79, 1.75, 1.86, 1.75, 1.59,
## 1.75, 1.89, 1.76, 1.89, 1.79, 1.86, 1.89, 1.75, 1.99, 1.69,
## 1.79, 1.99, 1.86, 1.75, 1.69, 1.79, 1.39, 1.79, 1.75, 1.86,
## 1.86, 1.39, 1.86, 1.75, 1.69, 1.86, 1.79, 1.76, 1.99, 1.86,
## 1.86, 1.86, 1.49, 1.75, 1.69, 1.75, 1.89, 1.39, 1.69, 1.86,
## 1.99, 1.99, 1.75, 1.79, 1.49, 1.89, 1.79, 1.99, 1.89, 1.75,
## 1.69, 1.69, 1.75, 1.99, 1.89, 1.99, 1.75, 1.79, 1.96, 1.86,
## 1.86, 1.86, 1.86, 1.75, 1.59, 1.69, 1.86, 1.79, 1.86, 1.79,
## 1.99, 1.99, 1.86, 1.86, 1.99, 1.86, 1.86, 1.99, 1.89, 1.99,
## 1.75, 1.79, 2.06, 1.39, 1.86, 1.86, 1.86, 1.79, 1.99, 1.89,
## 1.86, 1.75, 1.59, 1.59, 1.69, 1.99, 1.99, 1.99, 1.79, 1.69,
## 1.49, 1.75, 1.79, 1.75, 1.76, 1.86, 1.96, 1.75, 1.99, 1.89,
## 1.86, 1.86, 1.86, 1.75, 1.89, 1.96, 1.59, 1.86, 1.89, 1.96,
## 1.86, 1.86, 1.89, 1.75, 1.99, 1.99, 1.86, 1.79, 1.79, 1.99,
## 1.86, 1.69, 1.89, 1.99, 1.99, 1.86, 1.86, 1.69, 1.86, 1.76,
## 1.79, 2.06, 1.86, 1.89, 1.79, 1.86, 1.89, 1.86, 1.86, 1.86,
## 1.99, 1.86, 1.86, 1.49, 1.99, 1.86, 1.86, 1.76, 1.79, 1.86,
## 1.49, 1.69, 1.69, 1.76, 1.69, 1.99, 1.79, 1.89, 1.76, 1.86,
## 1.99, 1.49, 1.69, 1.75, 2.09, 1.79, 1.99, 1.69, 1.75, 1.79,
## 1.69, 1.75, 1.59, 1.86, 1.99, 1.96, 1.76, 1.99, 1.86, 1.86,
## 1.86, 1.86, 1.75, 1.99, 1.76, 1.86, 1.49, 1.69, 1.69, 1.69,
## 1.39, 1.86, 1.99, 1.75, 1.59, 1.76, 1.86, 1.99, 1.99, 1.99,
## 1.99, 1.86, 1.89, 1.86, 1.99, 1.39, 1.49, 1.99, 2.09, 1.99,
## 1.59, 1.99, 1.86, 1.89, 1.75, 1.59, 1.96, 1.75, 1.79, 1.86,
## 1.59, 1.69, 1.39, 1.86, 1.86, 2.06, 1.89, 1.86, 1.86, 1.75,
## 1.86, 1.89, 1.89, 1.86, 1.79, 1.89, 1.86, 1.86, 1.99, 1.99,
## 1.49, 1.76, 1.49, 1.86, 1.99, 1.76, 1.99, 1.79, 1.89, 1.89,
## 1.75, 1.76, 1.76, 1.99, 1.86, 1.79, 1.96, 1.86, 1.59, 1.89,
## 1.86, 1.69, 1.86, 1.89, 1.99, 1.75, 1.76, 1.76, 1.79, 1.39,
## 1.89, 1.86, 1.75, 1.86, 1.86, 1.76, 1.99, 1.75, 1.75, 1.39,
## 1.89, 1.99, 1.89, 1.39, 1.89), c(0.2, -0.1, 0.44, 0.24, 0.64,
## 0, -0.3, 0.32, 0.32, 0.27, 0.03, 0, -0.2, 0.54, 0.03, 0.2,
## 0.2, 0.33, 0.3, -0.4, 0.19, 0, 0.32, -0.16, -0.3, 0.33, 0.44,
## 0.64, -0.2, 0.42, 0.32, -0.27, 0.32, -0.16, 0.32, 0.03, 0,
## 0, 0.3, 0.3, 0.2, 0, -0.2, -0.58, 0.24, -0.06, 0.24, 0.2,
## 0.32, 0.2, 0.32, 0.3, 0.38, -0.08, 0.44, 0.3, -0.2, 0.07,
## 0, -0.4, 0.64, 0.1, -0.2, 0.2, -0.38, 0.24, 0.2, 0.32, 0.2,
## 0.26, -0.3, 0.03, 0.1, 0.32, -0.2, 0.03, 0.23, 0.3, 0, 0.26,
## 0.3, 0.3, 0.24, 0.3, 0.3, 0.1, 0.2, 0.42, 0.3, 0.24, -0.16,
## 0.27, 0.24, 0, 0.3, 0.3, 0.1, 0.42, 0.24, 0.54, -0.16, 0.3,
## -0.3, 0.2, 0.24, 0.2, 0.64, 0.26, 0.19, 0.64, 0.64, 0.2,
## 0, 0.24, 0.3, 0.54, 0.42, 0.23, 0.27, -0.2, 0.24, 0, -0.16,
## 0.23, -0.17, 0.32, 0.3, -0.06, 0.3, -0.57, 0.24, -0.06, 0.64,
## 0.1, -0.17, 0, 0.03, 0.03, 0.3, -0.16, -0.67, 0.2, 0.54,
## 0.26, 0.03, 0.2, 0.3, 0.33, 0.23, 0, -0.2, 0.2, 0.1, 0.27,
## 0, -0.28, -0.17, 0, 0.27, 0.23, 0, 0.27, 0, 0.64, 0.27, 0.4,
## 0.3, 0.27, 0.2, 0.24, 0.3, 0, -0.28, 0.3, -0.17, -0.2, 0.42,
## -0.4, 0, 0.23, 0.2, 0.24, 0.32, -0.08, 0.64, 0.3, 0.42, 0.23,
## 0.19, 0.03, 0.2, 0.24, 0.33, 0, 0.24, 0.23, 0.32, 0.32, 0.24,
## 0.1, 0.32, 0.27, 0.2, -0.3, 0.1, 0.3, 0.32, 0.32, 0.2, 0.32,
## 0.44, 0.1, 0.07, 0.2, -0.06, 0.03, 0.24, 0.33, 0.23, 0, -0.16,
## 0.32, 0.54, 0.3, 0.3, 0, 0.23, -0.57, -0.16, 0.32, -0.4,
## -0.16, -0.4, 0.2, -0.4, -0.2, -0.3, -0.2, 0.24, 0.26, 0,
## 0.64, -0.58, -0.3, 0.32, 0.33, 0, 0.24, -0.2, 0.44, 0.64,
## 0.3, -0.16, 0, 0.32, 0.1, 0.3, 0.23, -0.4, 0, 0.32, 0.32,
## 0.19, 0.3, 0, 0.27, -0.17, 0.2, 0.32, 0.2, 0.03, 0.2, 0.1,
## 0.33, 0.27, 0.64, 0.44, 0.19, 0.3, 0.27, 0.2, 0.3, -0.16,
## 0.32, 0.2, 0.42, 0.19, 0.2, 0.03, 0.64, 0, 0, -0.57, 0.32,
## -0.4, 0.44, 0.27, 0.32, 0.23, -0.2, 0.24, 0.32, 0.24, 0.32,
## 0.2, 0, -0.58, -0.38, 0.3, 0.32, 0.64, 0.32, -0.1, 0.44,
## 0.3, 0.44, 0.42, 0.24, -0.58, 0.2, 0.3, 0.24, -0.16, 0.3,
## 0.24, 0.3, 0.24, 0.32, 0.44, 0.2, -0.38, 0, -0.1, -0.57,
## 0.2, 0.23, 0, 0.03, 0.54, 0.19, 0.32, 0.1, 0.2, 0.32, -0.67,
## 0.38, 0.54, -0.2, 0.26, -0.16, 0.32, 0.64, 0.32, 0.03, 0.1,
## 0.32, 0.24, -0.3, 0.2, 0.3, 0.32, 0.3, 0.2, 0.03, 0.27, 0.64,
## 0, 0.03, 0.2, 0.2, -0.4, 0.54, -0.4, -0.16, -0.1, 0.2, -0.2,
## 0.1, 0.44, 0.24, -0.17, 0.3, 0.03, 0.32, 0.24, 0.3, 0, 0.33,
## 0.32, 0.64, 0.33, 0.3, 0.24, 0.64, -0.2, 0.42, -0.57, 0.26,
## 0.27, 0.1, 0.24, 0.2, 0.32, 0.3, 0.54, -0.2, 0.42, 0.44,
## 0.26, 0.24, 0.3, 0.2, 0.4, 0.24, 0.33, -0.57, -0.16, 0.32,
## 0.23, -0.2, 0, 0, 0.27, 0.03, -0.3, 0.2, 0.3, 0.13, 0, 0.64,
## 0.32, 0.32, 0.32, 0.42, 0.24, 0.32, -0.4, 0.32, 0.3, 0.3,
## -0.08, 0.23, 0.64, 0.32, 0.1, 0.24, 0.3, -0.2, -0.4, 0.27,
## -0.16, 0.42, 0.24, 0.1, 0.54, 0.23, 0.2, 0.32, -0.16, 0.24,
## -0.2, -0.3, 0.33, 0.42, 0.3, 0.24, 0.24, 0.24, 0.2, 0.24,
## -0.58, 0.24, 0, 0.23, 0.2, -0.67, 0.54, -0.17, 0.32, -0.57,
## 0.54, 0.2, 0.27, 0.64, 0.64, -0.06, 0.32, 0, 0.32, -0.2,
## 0.32, 0.2, 0.32, -0.57, 0.03, -0.17, 0.3, -0.58, 0.27, 0.3,
## 0, -0.06, 0.32, -0.16, 0.54, -0.16, 0.2, -0.17, 0.2, 0, 0.26,
## 0.2, -0.16, 0.1, 0.3, 0, 0.24, -0.08, -0.16, 0.3, 0.44, 0.2,
## 0, -0.16, 0.27, 0.26, 0.2, 0.26, -0.16, 0.3, 0.26, 0.3, 0.33,
## 0.19, 0.27, -0.38, -0.08, 0.64, -0.06, 0, 0.24, 0.2, 0.3,
## 0.3, 0.23, 0.3, 0.24, -0.06, 0.3, 0.64, 0.2, 0, -0.1, -0.2,
## 0.24, 0.3, 0, -0.06, -0.4, 0.2, 0.24, -0.06, 0.44, -0.57,
## -0.67, 0.32, 0.32, 0.32, 0.24, 0.54, 0.3, -0.08, 0.3, 0.32,
## 0.44, -0.3, 0.19, 0.32, 0.23, 0.24, 0.32, 0.32, 0.24, 0.2,
## 0.1, 0.24, 0.3, 0.07, 0.3, -0.28, -0.67, 0.32, 0.44, -0.4,
## 0.2, 0.32, -0.16, 0.54, 0.54, 0.3, 0.24, 0.1, -0.3, 0.44,
## 0.3, 0.64, -0.16, 0.3, -0.16, 0.33, 0.32, -0.58, -0.16, 0.24,
## 0.2, 0.32, 0.32, 0.03, -0.16, 0.2, -0.58, 0.54, 0.23, -0.2,
## -0.58, 0.32, 0.03, 0.2, -0.16, 0.3, 0.3, 0.27, 0, 0, -0.1,
## 0.32, 0, 0.2, -0.1, -0.4, -0.28, 0.23, 0, 0.32, -0.17, 0.3,
## 0.07, -0.08, 0.2, 0, -0.08, 0.2, 0.32, -0.38, 0.03, 0.3,
## 0.03, 0.27, 0.64, -0.4, 0.03, -0.07, 0.33, 0.3, 0.32, 0.64,
## 0.3, 0, 0.33, 0, 0.24, 0, 0.2, 0.13, 0.26, -0.3, 0.64, 0.3,
## -0.16, -0.4, 0.3, -0.3, 0, -0.16, 0.3, 0, 0.24, 0.54, -0.07,
## 0.24, -0.58, 0.42, -0.4, -0.17, 0.32, 0.32, -0.08, -0.16,
## -0.3, 0.33, 0.32, 0.64, 0, 0, 0, 0.2, 0.32, 0.24, 0.24, 0.54,
## 0.23, 0.32, 0.19, -0.3, -0.3, 0.24, -0.28, 0.2, 0.03, 0.24,
## 0.3, 0.64, 0.24, -0.4, 0.24, 0.1, 0.24, 0.32, -0.2, -0.06,
## 0.54, -0.58, -0.06, 0.3, 0.23, 0.54, 0, 0.2, 0.32, -0.17,
## 0.07, 0.2, 0.32, 0.32, -0.16, -0.67, 0.2, 0.2, -0.17, 0.3,
## -0.2, 0.27, 0.32, 0.24, 0.3, 0.64, 0.33, 0.64, 0.27, 0.3,
## 0.42, 0.24, 0.44, 0.2, -0.2, -0.16, 0.03, 0.33, -0.4, 0.32,
## 0, -0.58, 0.23, 0.1, 0.2, 0.23, -0.2, 0.32, 0.2, 0.24, -0.16,
## 0.33, 0.33, 0.3, 0.2, 0.2, 0.27, 0.24, 0.27, 0.03, 0.33,
## 0.3, -0.16, 0.24, 0.1, 0.2, 0.19, -0.2, 0.2, 0.2), c(0, 0,
## 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0,
## 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 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, 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, 0, 0, 1, 1, 0, 0, 0, 0, 0,
## 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1,
## 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0,
## 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
## 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0,
## 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
## 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1,
## 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0,
## 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0,
## 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,
## 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1,
## 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0,
## 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0,
## 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 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, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0,
## 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0,
## 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0,
## 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0,
## 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1,
## 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0,
## 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0,
## 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,
## 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1,
## 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0),
## c(0, 0.174672, 0, 0, 0, 0, 0.191388, 0, 0, 0, 0.112676, 0,
## 0.118343, 0, 0.100503, 0, 0.253521, 0, 0, 0.253521, 0, 0,
## 0, 0.201005, 0.191388, 0, 0, 0, 0.191388, 0, 0, 0.253521,
## 0, 0.201005, 0, 0.112676, 0, 0, 0, 0, 0, 0, 0.191388, 0.366972,
## 0, 0.150754, 0, 0, 0, 0, 0, 0, 0, 0.183486, 0, 0, 0.191388,
## 0, 0, 0.191388, 0, 0, 0.118343, 0.253521, 0.321101, 0, 0,
## 0, 0, 0.027523, 0.191388, 0.095694, 0, 0, 0.191388, 0.095694,
## 0, 0, 0, 0.027523, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.201005,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.201005, 0, 0.191388, 0, 0, 0,
## 0, 0.027523, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.191388, 0,
## 0, 0.201005, 0, 0.201005, 0, 0, 0.150754, 0, 0.347418, 0,
## 0.150754, 0, 0, 0.201005, 0, 0.050251, 0.095694, 0, 0.201005,
## 0.40201, 0, 0, 0.027523, 0.050251, 0, 0, 0, 0, 0, 0.191388,
## 0.253521, 0, 0, 0, 0.275229, 0.150754, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.275229, 0, 0.201005, 0.118343,
## 0, 0.253521, 0, 0, 0, 0, 0, 0.183486, 0, 0, 0, 0, 0, 0.050251,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.191388, 0, 0, 0,
## 0, 0, 0, 0, 0.150754, 0, 0.253521, 0.150754, 0.100503, 0,
## 0, 0, 0, 0.201005, 0, 0, 0, 0, 0, 0, 0.347418, 0.201005,
## 0, 0.253521, 0.201005, 0.253521, 0.253521, 0.191388, 0.191388,
## 0.191388, 0.118343, 0, 0.027523, 0, 0, 0.366972, 0.191388,
## 0, 0, 0, 0, 0.118343, 0, 0, 0, 0.201005, 0, 0, 0, 0, 0, 0.191388,
## 0, 0, 0, 0, 0, 0, 0, 0.150754, 0, 0, 0, 0.095694, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0.201005, 0, 0.253521, 0, 0, 0.253521,
## 0.112676, 0, 0, 0, 0.347418, 0, 0.253521, 0, 0, 0, 0, 0.118343,
## 0, 0, 0, 0, 0, 0, 0.366972, 0.321101, 0, 0, 0, 0, 0.174672,
## 0, 0, 0, 0, 0, 0.366972, 0, 0, 0, 0.201005, 0, 0, 0, 0, 0,
## 0, 0, 0.321101, 0, 0.201005, 0.347418, 0, 0, 0, 0.112676,
## 0, 0, 0, 0, 0.253521, 0, 0.40201, 0, 0, 0.191388, 0.027523,
## 0.201005, 0, 0, 0, 0.095694, 0, 0, 0, 0.191388, 0, 0, 0,
## 0, 0, 0.095694, 0, 0, 0, 0.095694, 0, 0, 0.253521, 0, 0.253521,
## 0.201005, 0.174672, 0, 0.191388, 0.118343, 0, 0, 0.201005,
## 0, 0.112676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.191388, 0,
## 0.347418, 0.027523, 0, 0, 0, 0, 0, 0, 0, 0.191388, 0, 0,
## 0.027523, 0, 0, 0.253521, 0, 0, 0, 0.347418, 0.201005, 0,
## 0, 0.191388, 0, 0, 0, 0.050251, 0.191388, 0, 0, 0.050251,
## 0, 0, 0, 0, 0, 0, 0, 0, 0.253521, 0, 0, 0, 0.183486, 0, 0,
## 0, 0, 0, 0, 0.118343, 0.253521, 0, 0.201005, 0, 0, 0, 0,
## 0, 0, 0, 0.201005, 0, 0.191388, 0.191388, 0, 0, 0, 0, 0,
## 0, 0, 0, 0.366972, 0, 0, 0, 0, 0.40201, 0, 0.201005, 0, 0.347418,
## 0, 0.253521, 0, 0, 0, 0.150754, 0, 0, 0, 0.118343, 0, 0.253521,
## 0, 0.347418, 0.112676, 0.150754, 0, 0.366972, 0, 0, 0, 0.150754,
## 0, 0.201005, 0, 0.201005, 0, 0.201005, 0, 0, 0.027523, 0,
## 0.201005, 0, 0, 0, 0, 0.183486, 0.201005, 0, 0, 0.253521,
## 0, 0.201005, 0, 0.027523, 0.253521, 0.027523, 0.201005, 0,
## 0.027523, 0, 0, 0, 0, 0.321101, 0.183486, 0, 0.150754, 0,
## 0, 0, 0, 0, 0, 0, 0, 0.150754, 0, 0, 0, 0, 0.174672, 0.191388,
## 0, 0, 0, 0.150754, 0.253521, 0, 0, 0.150754, 0, 0.347418,
## 0.40201, 0, 0, 0, 0, 0, 0, 0.183486, 0, 0, 0, 0.191388, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.275229, 0.40201, 0,
## 0, 0.253521, 0, 0, 0.201005, 0, 0, 0, 0, 0, 0.191388, 0,
## 0, 0, 0.201005, 0, 0.201005, 0, 0, 0.366972, 0.201005, 0,
## 0, 0, 0, 0.112676, 0.201005, 0, 0.366972, 0, 0, 0.191388,
## 0.366972, 0, 0.112676, 0, 0.201005, 0, 0, 0, 0, 0, 0.174672,
## 0, 0, 0, 0.174672, 0.253521, 0.275229, 0, 0, 0, 0.201005,
## 0, 0, 0.183486, 0, 0, 0.183486, 0, 0, 0.321101, 0.112676,
## 0, 0.112676, 0, 0, 0.253521, 0.112676, 0.100503, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0.050251, 0.027523, 0.191388, 0,
## 0, 0.201005, 0.191388, 0, 0.191388, 0, 0.201005, 0, 0, 0,
## 0, 0.100503, 0, 0.366972, 0, 0.253521, 0.150754, 0, 0, 0.183486,
## 0.201005, 0.191388, 0, 0, 0, 0, 0, 0, 0.253521, 0, 0, 0,
## 0, 0, 0, 0, 0.191388, 0.191388, 0, 0.275229, 0, 0.112676,
## 0, 0, 0, 0, 0.191388, 0, 0.150754, 0, 0, 0.191388, 0.150754,
## 0, 0.366972, 0.150754, 0, 0, 0, 0, 0.253521, 0, 0.150754,
## 0, 0, 0, 0, 0.201005, 0.40201, 0, 0, 0.150754, 0, 0.191388,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.191388, 0.201005,
## 0.100503, 0, 0.253521, 0, 0, 0.366972, 0, 0.150754, 0, 0,
## 0.118343, 0, 0, 0, 0.201005, 0, 0, 0, 0.253521, 0, 0, 0,
## 0, 0.050251, 0, 0, 0.201005, 0, 0.118343, 0, 0, 0.191388,
## 0.253521, 0), c(0, 0, 0, 0, 0.198925, 0, 0, 0, 0, 0, 0, 0,
## 0, 0.145161, 0, 0.050251, 0.252688, 0.053763, 0.177515, 0,
## 0, 0, 0, 0, 0, 0, 0, 0.198925, 0.095694, 0.068783, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.095694, 0, 0, 0, 0, 0, 0,
## 0.050251, 0, 0, 0.120603, 0, 0, 0, 0.095694, 0, 0, 0, 0.198925,
## 0, 0, 0.252688, 0, 0, 0.050251, 0, 0.050251, 0, 0, 0, 0,
## 0, 0.095694, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.050251, 0.068783,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.145161, 0, 0, 0, 0.050251,
## 0, 0.050251, 0.198925, 0, 0, 0.251256, 0.198925, 0, 0, 0,
## 0, 0.145161, 0, 0, 0, 0.095694, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0.198925, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.145161, 0,
## 0, 0.095694, 0, 0.068783, 0, 0, 0.095694, 0.252688, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.198925, 0, 0.091398, 0, 0, 0.050251,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.050251, 0, 0, 0, 0.251256,
## 0, 0.068783, 0, 0, 0, 0, 0, 0.068783, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0.095694, 0, 0, 0, 0, 0, 0.050251, 0, 0, 0.091429,
## 0, 0.252688, 0, 0, 0, 0.068783, 0, 0, 0, 0, 0.145161, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.252688, 0, 0.050251, 0, 0, 0,
## 0, 0, 0.198925, 0, 0, 0, 0, 0, 0, 0, 0, 0.198925, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.095694, 0, 0.050251,
## 0, 0.050251, 0, 0.068783, 0, 0.198925, 0, 0, 0, 0, 0.095694,
## 0, 0, 0, 0.252688, 0.068783, 0, 0.252688, 0, 0.251256, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0.198925, 0, 0, 0, 0, 0, 0, 0, 0, 0.050251, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0.050251, 0, 0, 0, 0, 0.050251, 0, 0, 0, 0.145161,
## 0, 0, 0, 0.252688, 0, 0, 0.120603, 0.145161, 0.095694, 0,
## 0, 0, 0.198925, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.095694, 0,
## 0, 0.198925, 0, 0, 0.095694, 0, 0, 0.145161, 0, 0, 0, 0,
## 0.050251, 0.177515, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.198925,
## 0.053763, 0, 0, 0.198925, 0.095694, 0, 0, 0, 0, 0, 0, 0.050251,
## 0, 0, 0.145161, 0.095694, 0.068783, 0, 0, 0, 0, 0.252688,
## 0.091398, 0, 0.053763, 0, 0, 0, 0, 0.095694, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0.198925, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0.198925, 0, 0, 0, 0, 0, 0, 0, 0, 0.068783, 0, 0, 0.145161,
## 0, 0, 0, 0, 0, 0.050251, 0, 0.053763, 0, 0, 0, 0, 0, 0.050251,
## 0, 0, 0, 0, 0, 0.050251, 0, 0.145161, 0, 0, 0, 0.145161,
## 0.252688, 0, 0.198925, 0.251256, 0, 0, 0, 0, 0, 0, 0.252688,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.145161, 0, 0.050251,
## 0, 0.050251, 0, 0, 0.050251, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.252688,
## 0, 0, 0, 0, 0.252688, 0, 0, 0, 0, 0, 0.068783, 0, 0, 0, 0,
## 0.198925, 0, 0, 0, 0, 0.177515, 0, 0, 0, 0, 0, 0, 0.251256,
## 0, 0, 0, 0.050251, 0, 0, 0, 0, 0, 0.050251, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0.145161, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0.050251, 0, 0, 0, 0, 0.177515, 0, 0, 0, 0, 0, 0.050251,
## 0, 0, 0.145161, 0.145161, 0, 0, 0, 0, 0, 0, 0.198925, 0,
## 0, 0, 0.068783, 0, 0, 0, 0, 0.050251, 0, 0, 0, 0, 0.050251,
## 0, 0.145161, 0, 0.050251, 0, 0, 0, 0.050251, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0.050251, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0.050251, 0, 0, 0, 0, 0, 0, 0.198925, 0, 0, 0, 0, 0,
## 0, 0.251256, 0, 0, 0.068783, 0, 0, 0, 0.050251, 0, 0, 0,
## 0.251256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.145161, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0.053763, 0, 0.251256, 0, 0, 0, 0.252688,
## 0, 0, 0, 0.145161, 0, 0, 0, 0, 0, 0, 0, 0.050251, 0, 0, 0.177515,
## 0.198925, 0, 0, 0, 0.091429, 0, 0, 0.050251, 0, 0.145161,
## 0, 0, 0, 0, 0.145161, 0, 0.252688, 0, 0, 0, 0, 0, 0, 0, 0,
## 0.050251, 0.050251, 0, 0, 0.095694, 0, 0, 0, 0, 0.198925,
## 0, 0.251256, 0, 0, 0.068783, 0, 0, 0.050251, 0.050251, 0,
## 0, 0, 0, 0, 0, 0, 0, 0.091429, 0.050251, 0, 0, 0, 0.050251,
## 0, 0, 0.068783, 0.053763, 0, 0.252688, 0.050251, 0, 0, 0,
## 0, 0.053763, 0, 0, 0, 0.177515, 0.050251, 0, 0.095694, 0.252688,
## 0.050251), c(0.2, 0.3, 0.44, 0.24, 0.27, 0, 0.1, 0.32, 0.32,
## 0.27, 0.27, 0, 0, 0.27, 0.23, 0.1, 0.27, 0.23, 0, 0.14, 0.19,
## 0, 0.32, 0.24, 0.1, 0.33, 0.44, 0.27, 0, 0.29, 0.32, 0.27,
## 0.32, 0.24, 0.32, 0.27, 0, 0, 0.3, 0.3, 0.2, 0, 0, 0.22,
## 0.24, 0.24, 0.24, 0.2, 0.32, 0.1, 0.32, 0.3, 0.14, 0.32,
## 0.44, 0.3, 0, 0.07, 0, 0, 0.27, 0.1, 0, 0.27, 0.32, 0.24,
## 0.1, 0.32, 0.1, 0.32, 0.1, 0.23, 0.1, 0.32, 0, 0.23, 0.23,
## 0.3, 0, 0.32, 0.3, 0.3, 0.24, 0.3, 0.3, 0.1, 0.1, 0.29, 0.3,
## 0.24, 0.24, 0.27, 0.24, 0, 0.3, 0.3, 0.1, 0.42, 0.24, 0.27,
## 0.24, 0.3, 0.1, 0.1, 0.24, 0.1, 0.27, 0.32, 0.19, 0.14, 0.27,
## 0.2, 0, 0.24, 0.3, 0.27, 0.42, 0.23, 0.27, 0, 0.24, 0, 0.24,
## 0.23, 0.23, 0.32, 0.3, 0.24, 0.3, 0.17, 0.24, 0.24, 0.27,
## 0.1, 0.23, 0, 0.13, 0.23, 0.3, 0.24, 0.13, 0.2, 0.27, 0.32,
## 0.13, 0, 0.3, 0.2, 0.23, 0, 0, 0.27, 0.1, 0.27, 0, 0.32,
## 0.13, 0, 0.27, 0.23, 0, 0.27, 0, 0.27, 0.27, 0.23, 0.3, 0.27,
## 0.1, 0.24, 0.3, 0, 0.32, 0.3, 0.23, 0, 0.42, 0.14, 0, 0.23,
## 0.1, 0.24, 0.32, 0.32, 0.14, 0.3, 0.29, 0.23, 0.19, 0.13,
## 0.2, 0.24, 0.2, 0, 0.24, 0.23, 0.32, 0.32, 0.24, 0.1, 0.32,
## 0.27, 0, 0.1, 0.1, 0.3, 0.32, 0.32, 0.1, 0.32, 0.44, 0.24,
## 0.07, 0.27, 0.24, 0.23, 0.24, 0.2, 0.23, 0, 0.24, 0.32, 0.27,
## 0.3, 0.3, 0, 0.23, 0.17, 0.24, 0.32, 0.14, 0.24, 0.14, 0.27,
## 0, 0.1, 0.1, 0, 0.24, 0.32, 0, 0.27, 0.22, 0.1, 0.32, 0.33,
## 0, 0.24, 0, 0.44, 0.27, 0.3, 0.24, 0, 0.32, 0.1, 0.3, 0.23,
## 0, 0, 0.32, 0.32, 0.19, 0.3, 0, 0.27, 0.13, 0, 0.32, 0.1,
## 0.23, 0.1, 0.1, 0.2, 0.27, 0.27, 0.44, 0.19, 0.3, 0.27, 0,
## 0.3, 0.24, 0.32, 0.27, 0.29, 0.19, 0.27, 0.27, 0.14, 0, 0,
## 0.17, 0.32, 0.14, 0.44, 0.27, 0.32, 0.23, 0, 0.24, 0.32,
## 0.24, 0.32, 0.2, 0, 0.22, 0.32, 0.3, 0.32, 0.27, 0.32, 0.3,
## 0.44, 0.3, 0.44, 0.42, 0.24, 0.22, 0.1, 0.3, 0.24, 0.24,
## 0.3, 0.24, 0.3, 0.24, 0.32, 0.44, 0.1, 0.32, 0, 0.3, 0.17,
## 0.1, 0.23, 0, 0.27, 0.27, 0.19, 0.32, 0.1, 0.27, 0.32, 0.13,
## 0.14, 0.27, 0, 0.32, 0.24, 0.32, 0.27, 0.32, 0.23, 0.1, 0.32,
## 0.24, 0.1, 0.2, 0.3, 0.32, 0.3, 0, 0.23, 0.27, 0.27, 0, 0.23,
## 0, 0.2, 0.14, 0.27, 0.14, 0.24, 0.3, 0.2, 0.1, 0, 0.44, 0.24,
## 0.23, 0.3, 0.27, 0.32, 0.24, 0.3, 0, 0.33, 0.32, 0.27, 0.23,
## 0.3, 0.24, 0.27, 0, 0.42, 0.17, 0.32, 0.27, 0.1, 0.24, 0.1,
## 0.32, 0.3, 0.27, 0, 0.29, 0.44, 0.32, 0.24, 0.3, 0.27, 0.23,
## 0.24, 0.23, 0.17, 0.24, 0.32, 0.23, 0, 0, 0, 0.27, 0.13,
## 0.1, 0.2, 0.3, 0.23, 0, 0.27, 0.32, 0.32, 0.32, 0.42, 0.24,
## 0.32, 0.14, 0.32, 0.3, 0.3, 0.32, 0.23, 0.27, 0.32, 0.1,
## 0.24, 0.3, 0, 0.14, 0.27, 0.24, 0.29, 0.24, 0.1, 0.27, 0.23,
## 0.2, 0.32, 0.24, 0.24, 0.1, 0.1, 0.23, 0.42, 0.3, 0.24, 0.24,
## 0.24, 0.1, 0.24, 0.22, 0.24, 0, 0.23, 0.1, 0.13, 0.27, 0.23,
## 0.32, 0.17, 0.27, 0.27, 0.27, 0.27, 0.14, 0.24, 0.32, 0,
## 0.32, 0, 0.32, 0.27, 0.32, 0.17, 0.27, 0.13, 0.3, 0.22, 0.27,
## 0.3, 0, 0.24, 0.32, 0.24, 0.27, 0.24, 0.1, 0.23, 0.1, 0,
## 0.32, 0.1, 0.24, 0.1, 0.3, 0, 0.24, 0.32, 0.24, 0.3, 0.44,
## 0.27, 0, 0.24, 0.27, 0.32, 0.27, 0.32, 0.24, 0.3, 0.32, 0.3,
## 0.2, 0.19, 0.27, 0.32, 0.32, 0.27, 0.24, 0, 0.24, 0.2, 0,
## 0.3, 0.23, 0.3, 0.24, 0.24, 0.3, 0.14, 0.2, 0, 0.3, 0.1,
## 0.24, 0.3, 0, 0.24, 0.14, 0.1, 0.24, 0.24, 0.44, 0.17, 0.13,
## 0.32, 0.32, 0.32, 0.24, 0.27, 0.3, 0.32, 0.3, 0.32, 0.44,
## 0.1, 0.19, 0.32, 0.23, 0.24, 0.32, 0.32, 0.24, 0.1, 0.1,
## 0.24, 0.3, 0.07, 0, 0.32, 0.13, 0.32, 0.44, 0.14, 0.1, 0.32,
## 0.24, 0.27, 0.27, 0.3, 0.24, 0.1, 0.1, 0.44, 0.3, 0.27, 0.24,
## 0.3, 0.24, 0.2, 0.32, 0.22, 0.24, 0.24, 0.1, 0.32, 0.32,
## 0.27, 0.24, 0.1, 0.22, 0.27, 0.23, 0.1, 0.22, 0.32, 0.27,
## 0.1, 0.24, 0.3, 0.3, 0.27, 0, 0, 0.3, 0.32, 0, 0.1, 0.3,
## 0.14, 0.32, 0.23, 0, 0.32, 0.23, 0.3, 0.07, 0.32, 0.2, 0,
## 0.32, 0.1, 0.32, 0.32, 0.27, 0.3, 0.27, 0.27, 0.27, 0.14,
## 0.27, 0.13, 0.33, 0.3, 0.32, 0.14, 0.3, 0, 0.2, 0, 0.24,
## 0, 0.1, 0.23, 0.32, 0.1, 0.14, 0.3, 0.24, 0, 0.3, 0.1, 0,
## 0.24, 0.3, 0, 0.24, 0.27, 0.13, 0.24, 0.22, 0.42, 0.14, 0.13,
## 0.32, 0.32, 0.32, 0.24, 0.1, 0.23, 0.32, 0.14, 0, 0, 0, 0.27,
## 0.32, 0.24, 0.24, 0.27, 0.23, 0.32, 0.19, 0.1, 0.1, 0.24,
## 0.32, 0.1, 0.27, 0.24, 0, 0.27, 0.24, 0, 0.24, 0.24, 0.24,
## 0.32, 0.1, 0.24, 0.27, 0.22, 0.24, 0.3, 0.23, 0.27, 0, 0.27,
## 0.32, 0.13, 0.07, 0.2, 0.32, 0.32, 0.24, 0.13, 0.1, 0.1,
## 0.13, 0.3, 0, 0.27, 0.32, 0.24, 0.3, 0.27, 0.33, 0.14, 0.27,
## 0.3, 0.29, 0.24, 0.44, 0.1, 0.1, 0.24, 0.23, 0.33, 0.14,
## 0.32, 0, 0.22, 0.23, 0.24, 0.1, 0.23, 0, 0.32, 0.1, 0.24,
## 0.24, 0.2, 0.23, 0.3, 0.27, 0.1, 0.27, 0.24, 0.27, 0.13,
## 0.23, 0.3, 0.24, 0.24, 0, 0.1, 0.19, 0, 0.27, 0.1), c(2,
## 3, 3, 4, 0, 4, 4, 1, 0, 0, 0, 4, 0, 0, 1, 3, 0, 0, 2, 0,
## 2, 4, 0, 0, 4, 1, 3, 0, 3, 2, 2, 0, 2, 0, 2, 0, 1, 2, 1,
## 3, 2, 4, 3, 2, 1, 2, 3, 2, 2, 4, 2, 4, 1, 2, 3, 2, 4, 0,
## 4, 4, 0, 3, 1, 0, 2, 2, 4, 2, 4, 2, 3, 0, 4, 2, 3, 0, 1,
## 2, 2, 2, 4, 1, 4, 4, 1, 3, 3, 2, 4, 3, 0, 0, 1, 2, 1, 3,
## 4, 1, 3, 0, 0, 1, 3, 3, 1, 3, 0, 2, 2, 0, 0, 2, 4, 2, 0,
## 0, 1, 0, 0, 4, 3, 3, 0, 0, 1, 1, 1, 1, 0, 1, 4, 1, 0, 3,
## 1, 2, 1, 0, 3, 0, 1, 2, 0, 2, 1, 3, 1, 2, 1, 2, 3, 0, 4,
## 0, 3, 2, 1, 4, 0, 0, 4, 0, 2, 0, 0, 1, 3, 0, 4, 3, 3, 3,
## 2, 3, 1, 0, 1, 0, 2, 2, 4, 4, 2, 2, 0, 3, 2, 0, 2, 1, 2,
## 3, 2, 3, 3, 0, 0, 0, 4, 4, 0, 0, 4, 3, 4, 3, 2, 2, 4, 1,
## 3, 2, 0, 0, 1, 1, 3, 2, 0, 2, 0, 2, 0, 3, 4, 4, 1, 1, 0,
## 1, 0, 0, 0, 0, 3, 3, 3, 0, 3, 2, 0, 0, 2, 4, 0, 1, 1, 2,
## 0, 3, 0, 3, 0, 4, 0, 3, 4, 0, 4, 4, 0, 0, 2, 1, 3, 0, 1,
## 3, 2, 3, 0, 3, 4, 2, 0, 0, 3, 2, 1, 0, 3, 0, 0, 0, 0, 2,
## 2, 0, 0, 0, 3, 3, 1, 1, 0, 3, 0, 2, 2, 0, 4, 2, 2, 0, 2,
## 3, 2, 2, 1, 0, 0, 1, 3, 4, 3, 4, 1, 3, 2, 3, 4, 2, 0, 0,
## 4, 3, 4, 0, 3, 4, 2, 2, 0, 1, 3, 1, 2, 0, 0, 2, 0, 3, 0,
## 0, 1, 1, 0, 4, 2, 0, 1, 0, 1, 0, 4, 0, 3, 4, 2, 3, 0, 4,
## 3, 0, 0, 0, 3, 0, 4, 2, 0, 0, 0, 0, 3, 2, 3, 1, 3, 3, 1,
## 4, 0, 2, 2, 4, 1, 1, 2, 0, 0, 1, 3, 0, 3, 1, 1, 2, 0, 4,
## 4, 3, 0, 4, 0, 4, 2, 4, 2, 4, 3, 0, 1, 1, 0, 1, 0, 0, 0,
## 4, 2, 2, 0, 1, 3, 2, 3, 1, 3, 0, 0, 0, 0, 1, 3, 0, 0, 0,
## 1, 3, 2, 1, 0, 2, 4, 4, 3, 0, 0, 0, 0, 2, 3, 3, 0, 1, 2,
## 2, 0, 4, 4, 4, 0, 1, 3, 2, 1, 2, 4, 3, 2, 1, 2, 1, 3, 1,
## 0, 1, 2, 1, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 1, 0,
## 1, 3, 2, 0, 3, 4, 2, 0, 0, 0, 0, 3, 1, 4, 3, 2, 4, 0, 3,
## 1, 4, 4, 2, 0, 2, 4, 0, 3, 0, 0, 2, 0, 2, 0, 2, 2, 3, 2,
## 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 4, 3, 1, 3, 0, 2, 3,
## 3, 4, 2, 0, 1, 2, 0, 4, 3, 2, 3, 1, 1, 0, 0, 1, 2, 0, 0,
## 2, 3, 0, 3, 4, 2, 0, 2, 3, 2, 0, 4, 4, 3, 2, 3, 0, 2, 2,
## 1, 0, 3, 0, 4, 2, 0, 0, 0, 1, 3, 4, 3, 3, 0, 0, 0, 3, 0,
## 2, 2, 2, 0, 3, 4, 2, 0, 0, 0, 3, 2, 0, 0, 3, 2, 2, 0, 4,
## 0, 3, 4, 0, 3, 3, 4, 0, 0, 3, 4, 0, 2, 1, 2, 0, 1, 0, 0,
## 2, 2, 4, 2, 4, 1, 2, 0, 4, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0,
## 0, 2, 2, 2, 3, 3, 3, 1, 2, 3, 0, 0, 0, 4, 3, 4, 2, 0, 0,
## 1, 2, 0, 1, 3, 2, 1, 0, 1, 0, 0, 2, 0, 4, 0, 0, 0, 2, 1,
## 2, 0, 0, 3, 1, 0, 1, 1, 2, 4, 4, 4, 2, 3, 0, 3, 2, 0, 3,
## 3, 3, 2, 4, 0, 3, 1, 0, 2, 1, 3, 0, 0, 2, 0, 1, 1, 0, 2,
## 1, 2, 0, 1, 3, 3, 1, 3, 4, 0, 0, 3, 4, 0, 1, 0, 0, 4, 2,
## 4, 4, 4, 4, 0, 1, 1, 0, 2, 3, 2, 1, 2, 3, 1, 1, 0, 3, 3,
## 0, 2, 0, 4, 0, 4, 0, 2, 0, 1, 0, 3, 0, 2, 1, 4, 2, 4, 0,
## 3), c(2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1,
## 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1,
## 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2,
## 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2,
## 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2,
## 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1,
## 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2,
## 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,
## 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1,
## 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1,
## 1, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1,
## 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1,
## 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2,
## 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1,
## 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1,
## 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1,
## 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1,
## 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1,
## 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1,
## 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1,
## 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1,
## 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1,
## 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1,
## 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2,
## 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2,
## 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1,
## 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1,
## 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2,
## 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1,
## 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2,
## 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1,
## 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1,
## 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1,
## 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2,
## 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1,
## 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1,
## 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2,
## 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 1, 1, 2)), control = list(20, 7, 0, 4, 5, 2, 0, 30, 0))
## n= 800
##
## CP nsplit rel error
## 1 0.529220779 0 1.0000000
## 2 0.015151515 1 0.4707792
## 3 0.008658009 4 0.4253247
## 4 0.008116883 9 0.3798701
## 5 0.003246753 11 0.3636364
## 6 0.001000000 17 0.3441558
##
## Variable importance
## LoyalCH PriceDiff SalePriceMM ListPriceDiff PriceMM
## 52 8 6 5 4
## DiscMM PctDiscMM StoreID SalePriceCH PriceCH
## 4 4 3 2 2
## PctDiscCH WeekofPurchase DiscCH STORE SpecialCH
## 2 2 2 1 1
## Store7Yes
## 1
##
## Node number 1: 800 observations, complexity param=0.5292208
## predicted class=CH expected loss=0.385 P(node) =1
## class counts: 492 308
## probabilities: 0.615 0.385
## left son=2 (515 obs) right son=3 (285 obs)
## Primary splits:
## LoyalCH < 0.48285 to the right, improve=142.35420, (0 missing)
## StoreID < 3.5 to the right, improve= 38.92912, (0 missing)
## PriceDiff < 0.015 to the right, improve= 21.29666, (0 missing)
## Store7Yes < 0.5 to the right, improve= 20.47828, (0 missing)
## STORE < 0.5 to the left, improve= 20.47828, (0 missing)
## Surrogate splits:
## DiscMM < 0.57 to the left, agree=0.652, adj=0.025, (0 split)
## PctDiscMM < 0.264375 to the left, agree=0.652, adj=0.025, (0 split)
## PriceMM < 1.89 to the right, agree=0.651, adj=0.021, (0 split)
## SalePriceMM < 1.385 to the right, agree=0.651, adj=0.021, (0 split)
## PriceDiff < -0.575 to the right, agree=0.651, adj=0.021, (0 split)
##
## Node number 2: 515 observations, complexity param=0.01515152
## predicted class=CH expected loss=0.1631068 P(node) =0.64375
## class counts: 431 84
## probabilities: 0.837 0.163
## left son=4 (313 obs) right son=5 (202 obs)
## Primary splits:
## LoyalCH < 0.705699 to the right, improve=16.736450, (0 missing)
## PriceDiff < 0.015 to the right, improve=10.207720, (0 missing)
## SalePriceMM < 2.125 to the right, improve= 8.685844, (0 missing)
## ListPriceDiff < 0.255 to the right, improve= 7.226422, (0 missing)
## PriceMM < 2.04 to the right, improve= 5.060421, (0 missing)
## Surrogate splits:
## WeekofPurchase < 237.5 to the right, agree=0.674, adj=0.168, (0 split)
## PriceCH < 1.755 to the right, agree=0.662, adj=0.139, (0 split)
## PriceMM < 2.04 to the right, agree=0.662, adj=0.139, (0 split)
## SalePriceMM < 1.64 to the right, agree=0.629, adj=0.054, (0 split)
## SalePriceCH < 1.775 to the right, agree=0.621, adj=0.035, (0 split)
##
## Node number 3: 285 observations, complexity param=0.008658009
## predicted class=MM expected loss=0.2140351 P(node) =0.35625
## class counts: 61 224
## probabilities: 0.214 0.786
## left son=6 (127 obs) right son=7 (158 obs)
## Primary splits:
## LoyalCH < 0.2761415 to the right, improve=9.017989, (0 missing)
## STORE < 1.5 to the left, improve=4.345310, (0 missing)
## StoreID < 3.5 to the right, improve=3.259297, (0 missing)
## SpecialCH < 0.5 to the right, improve=3.128141, (0 missing)
## PriceDiff < 0.54 to the right, improve=2.780319, (0 missing)
## Surrogate splits:
## STORE < 1.5 to the left, agree=0.649, adj=0.213, (0 split)
## StoreID < 1.5 to the left, agree=0.639, adj=0.189, (0 split)
## DiscMM < 0.08 to the right, agree=0.586, adj=0.071, (0 split)
## PctDiscMM < 0.038887 to the right, agree=0.586, adj=0.071, (0 split)
## SalePriceMM < 1.64 to the left, agree=0.582, adj=0.063, (0 split)
##
## Node number 4: 313 observations, complexity param=0.003246753
## predicted class=CH expected loss=0.06070288 P(node) =0.39125
## class counts: 294 19
## probabilities: 0.939 0.061
## left son=8 (298 obs) right son=9 (15 obs)
## Primary splits:
## PriceDiff < -0.39 to the right, improve=7.038705, (0 missing)
## DiscMM < 0.47 to the left, improve=3.137527, (0 missing)
## PctDiscMM < 0.227263 to the left, improve=3.137527, (0 missing)
## SalePriceMM < 1.485 to the right, improve=2.729109, (0 missing)
## SalePriceCH < 1.925 to the left, improve=1.630667, (0 missing)
## Surrogate splits:
## DiscMM < 0.72 to the left, agree=0.971, adj=0.4, (0 split)
## SalePriceMM < 1.435 to the right, agree=0.971, adj=0.4, (0 split)
## PctDiscMM < 0.3342595 to the left, agree=0.971, adj=0.4, (0 split)
## SalePriceCH < 2.075 to the left, agree=0.962, adj=0.2, (0 split)
##
## Node number 5: 202 observations, complexity param=0.01515152
## predicted class=CH expected loss=0.3217822 P(node) =0.2525
## class counts: 137 65
## probabilities: 0.678 0.322
## left son=10 (120 obs) right son=11 (82 obs)
## Primary splits:
## ListPriceDiff < 0.235 to the right, improve=11.332540, (0 missing)
## PriceDiff < 0.265 to the right, improve=10.907380, (0 missing)
## SalePriceMM < 2.125 to the right, improve= 8.724531, (0 missing)
## PriceMM < 2.11 to the right, improve= 5.157551, (0 missing)
## DiscCH < 0.115 to the right, improve= 4.328572, (0 missing)
## Surrogate splits:
## PriceDiff < 0.235 to the right, agree=0.787, adj=0.476, (0 split)
## PriceMM < 1.89 to the right, agree=0.713, adj=0.293, (0 split)
## PriceCH < 1.875 to the left, agree=0.688, adj=0.232, (0 split)
## SalePriceMM < 2.105 to the right, agree=0.688, adj=0.232, (0 split)
## SalePriceCH < 1.875 to the left, agree=0.688, adj=0.232, (0 split)
##
## Node number 6: 127 observations, complexity param=0.008658009
## predicted class=MM expected loss=0.3543307 P(node) =0.15875
## class counts: 45 82
## probabilities: 0.354 0.646
## left son=12 (51 obs) right son=13 (76 obs)
## Primary splits:
## SalePriceMM < 2.04 to the right, improve=5.224787, (0 missing)
## PriceDiff < 0.05 to the right, improve=5.021004, (0 missing)
## DiscMM < 0.22 to the left, improve=2.781501, (0 missing)
## LoyalCH < 0.3146215 to the left, improve=2.593997, (0 missing)
## PctDiscMM < 0.0729725 to the left, improve=2.432729, (0 missing)
## Surrogate splits:
## PriceDiff < 0.16 to the right, agree=0.882, adj=0.706, (0 split)
## PriceMM < 2.04 to the right, agree=0.795, adj=0.490, (0 split)
## DiscMM < 0.08 to the left, agree=0.780, adj=0.451, (0 split)
## PctDiscMM < 0.038887 to the left, agree=0.780, adj=0.451, (0 split)
## ListPriceDiff < 0.28 to the right, agree=0.724, adj=0.314, (0 split)
##
## Node number 7: 158 observations
## predicted class=MM expected loss=0.1012658 P(node) =0.1975
## class counts: 16 142
## probabilities: 0.101 0.899
##
## Node number 8: 298 observations
## predicted class=CH expected loss=0.03691275 P(node) =0.3725
## class counts: 287 11
## probabilities: 0.963 0.037
##
## Node number 9: 15 observations
## predicted class=MM expected loss=0.4666667 P(node) =0.01875
## class counts: 7 8
## probabilities: 0.467 0.533
##
## Node number 10: 120 observations, complexity param=0.003246753
## predicted class=CH expected loss=0.1833333 P(node) =0.15
## class counts: 98 22
## probabilities: 0.817 0.183
## left son=20 (40 obs) right son=21 (80 obs)
## Primary splits:
## PriceDiff < 0.31 to the right, improve=2.133333, (0 missing)
## StoreID < 2.5 to the right, improve=2.126756, (0 missing)
## SalePriceMM < 2.04 to the right, improve=2.028356, (0 missing)
## PriceCH < 1.755 to the right, improve=1.951305, (0 missing)
## PriceMM < 2.04 to the right, improve=1.951305, (0 missing)
## Surrogate splits:
## SalePriceMM < 2.125 to the right, agree=0.842, adj=0.525, (0 split)
## ListPriceDiff < 0.31 to the right, agree=0.825, adj=0.475, (0 split)
## WeekofPurchase < 252.5 to the right, agree=0.758, adj=0.275, (0 split)
## PriceMM < 2.155 to the right, agree=0.708, adj=0.125, (0 split)
## DiscCH < 0.065 to the right, agree=0.708, adj=0.125, (0 split)
##
## Node number 11: 82 observations, complexity param=0.01515152
## predicted class=MM expected loss=0.4756098 P(node) =0.1025
## class counts: 39 43
## probabilities: 0.476 0.524
## left son=22 (12 obs) right son=23 (70 obs)
## Primary splits:
## PctDiscCH < 0.052007 to the right, improve=5.469106, (0 missing)
## DiscCH < 0.115 to the right, improve=4.875412, (0 missing)
## PriceDiff < 0.215 to the right, improve=3.597677, (0 missing)
## PctDiscMM < 0.1961965 to the left, improve=2.305800, (0 missing)
## DiscMM < 0.25 to the left, improve=2.035928, (0 missing)
## Surrogate splits:
## PriceDiff < 0.265 to the right, agree=0.963, adj=0.750, (0 split)
## DiscCH < 0.115 to the right, agree=0.951, adj=0.667, (0 split)
## PriceCH < 2.075 to the right, agree=0.878, adj=0.167, (0 split)
## SalePriceCH < 1.54 to the left, agree=0.878, adj=0.167, (0 split)
##
## Node number 12: 51 observations, complexity param=0.008658009
## predicted class=CH expected loss=0.4705882 P(node) =0.06375
## class counts: 27 24
## probabilities: 0.529 0.471
## left son=24 (20 obs) right son=25 (31 obs)
## Primary splits:
## PriceMM < 2.155 to the left, improve=1.914991, (0 missing)
## SalePriceMM < 2.155 to the left, improve=1.797345, (0 missing)
## StoreID < 1.5 to the left, improve=1.348273, (0 missing)
## STORE < 1.5 to the left, improve=1.345098, (0 missing)
## WeekofPurchase < 264 to the right, improve=0.956926, (0 missing)
## Surrogate splits:
## SalePriceMM < 2.155 to the left, agree=0.961, adj=0.90, (0 split)
## SalePriceCH < 1.825 to the left, agree=0.804, adj=0.50, (0 split)
## ListPriceDiff < 0.235 to the left, agree=0.784, adj=0.45, (0 split)
## PriceDiff < 0.325 to the right, agree=0.745, adj=0.35, (0 split)
## STORE < 1.5 to the left, agree=0.745, adj=0.35, (0 split)
##
## Node number 13: 76 observations, complexity param=0.008658009
## predicted class=MM expected loss=0.2368421 P(node) =0.095
## class counts: 18 58
## probabilities: 0.237 0.763
## left son=26 (13 obs) right son=27 (63 obs)
## Primary splits:
## SpecialCH < 0.5 to the right, improve=4.494441, (0 missing)
## DiscCH < 0.05 to the right, improve=1.594896, (0 missing)
## PctDiscCH < 0.0251255 to the right, improve=1.594896, (0 missing)
## PriceMM < 2.11 to the left, improve=1.387941, (0 missing)
## PriceDiff < -0.24 to the right, improve=1.387941, (0 missing)
## Surrogate splits:
## DiscCH < 0.25 to the right, agree=0.882, adj=0.308, (0 split)
## SalePriceCH < 1.49 to the left, agree=0.882, adj=0.308, (0 split)
## PctDiscCH < 0.1366045 to the right, agree=0.882, adj=0.308, (0 split)
##
## Node number 20: 40 observations
## predicted class=CH expected loss=0.05 P(node) =0.05
## class counts: 38 2
## probabilities: 0.950 0.050
##
## Node number 21: 80 observations, complexity param=0.003246753
## predicted class=CH expected loss=0.25 P(node) =0.1
## class counts: 60 20
## probabilities: 0.750 0.250
## left son=42 (56 obs) right son=43 (24 obs)
## Primary splits:
## StoreID < 2.5 to the right, improve=2.9761900, (0 missing)
## LoyalCH < 0.67808 to the left, improve=2.5000000, (0 missing)
## ListPriceDiff < 0.31 to the left, improve=1.1111110, (0 missing)
## STORE < 2.5 to the right, improve=0.7836991, (0 missing)
## Store7Yes < 0.5 to the right, improve=0.6393862, (0 missing)
## Surrogate splits:
## ListPriceDiff < 0.31 to the left, agree=0.800, adj=0.333, (0 split)
## SpecialMM < 0.5 to the left, agree=0.750, adj=0.167, (0 split)
## LoyalCH < 0.4924895 to the right, agree=0.725, adj=0.083, (0 split)
## Store7Yes < 0.5 to the right, agree=0.725, adj=0.083, (0 split)
## STORE < 0.5 to the left, agree=0.725, adj=0.083, (0 split)
##
## Node number 22: 12 observations
## predicted class=CH expected loss=0.08333333 P(node) =0.015
## class counts: 11 1
## probabilities: 0.917 0.083
##
## Node number 23: 70 observations, complexity param=0.008116883
## predicted class=MM expected loss=0.4 P(node) =0.0875
## class counts: 28 42
## probabilities: 0.400 0.600
## left son=46 (41 obs) right son=47 (29 obs)
## Primary splits:
## LoyalCH < 0.5945395 to the right, improve=1.525988, (0 missing)
## PriceDiff < -0.035 to the right, improve=1.414685, (0 missing)
## SalePriceMM < 1.74 to the right, improve=1.322222, (0 missing)
## DiscMM < 0.25 to the left, improve=1.260000, (0 missing)
## PctDiscMM < 0.1345485 to the left, improve=1.260000, (0 missing)
## Surrogate splits:
## WeekofPurchase < 246.5 to the right, agree=0.714, adj=0.310, (0 split)
## PriceMM < 1.89 to the right, agree=0.671, adj=0.207, (0 split)
## ListPriceDiff < 0.035 to the right, agree=0.671, adj=0.207, (0 split)
## PriceCH < 1.875 to the right, agree=0.657, adj=0.172, (0 split)
## SalePriceCH < 1.875 to the right, agree=0.657, adj=0.172, (0 split)
##
## Node number 24: 20 observations
## predicted class=CH expected loss=0.3 P(node) =0.025
## class counts: 14 6
## probabilities: 0.700 0.300
##
## Node number 25: 31 observations, complexity param=0.008658009
## predicted class=MM expected loss=0.4193548 P(node) =0.03875
## class counts: 13 18
## probabilities: 0.419 0.581
## left son=50 (7 obs) right son=51 (24 obs)
## Primary splits:
## LoyalCH < 0.424473 to the right, improve=1.5729650, (0 missing)
## WeekofPurchase < 256.5 to the right, improve=0.5583127, (0 missing)
## StoreID < 2.5 to the left, improve=0.4301075, (0 missing)
## ListPriceDiff < 0.295 to the right, improve=0.4205837, (0 missing)
## STORE < 1.5 to the left, improve=0.4182028, (0 missing)
## Surrogate splits:
## WeekofPurchase < 271 to the right, agree=0.871, adj=0.429, (0 split)
## DiscMM < 0.03 to the right, agree=0.839, adj=0.286, (0 split)
## SalePriceMM < 2.15 to the left, agree=0.839, adj=0.286, (0 split)
## PctDiscMM < 0.0137615 to the right, agree=0.839, adj=0.286, (0 split)
## StoreID < 1.5 to the left, agree=0.806, adj=0.143, (0 split)
##
## Node number 26: 13 observations
## predicted class=CH expected loss=0.3846154 P(node) =0.01625
## class counts: 8 5
## probabilities: 0.615 0.385
##
## Node number 27: 63 observations
## predicted class=MM expected loss=0.1587302 P(node) =0.07875
## class counts: 10 53
## probabilities: 0.159 0.841
##
## Node number 42: 56 observations
## predicted class=CH expected loss=0.1607143 P(node) =0.07
## class counts: 47 9
## probabilities: 0.839 0.161
##
## Node number 43: 24 observations, complexity param=0.003246753
## predicted class=CH expected loss=0.4583333 P(node) =0.03
## class counts: 13 11
## probabilities: 0.542 0.458
## left son=86 (17 obs) right son=87 (7 obs)
## Primary splits:
## LoyalCH < 0.635456 to the left, improve=1.2948180, (0 missing)
## WeekofPurchase < 236.5 to the right, improve=0.6666667, (0 missing)
## DiscMM < 0.18 to the right, improve=0.1666667, (0 missing)
## SpecialMM < 0.5 to the right, improve=0.1666667, (0 missing)
## SalePriceMM < 1.885 to the left, improve=0.1666667, (0 missing)
## Surrogate splits:
## DiscMM < 0.35 to the left, agree=0.792, adj=0.286, (0 split)
## PriceDiff < -0.07 to the right, agree=0.792, adj=0.286, (0 split)
## PctDiscMM < 0.16712 to the left, agree=0.792, adj=0.286, (0 split)
##
## Node number 46: 41 observations, complexity param=0.008116883
## predicted class=MM expected loss=0.4878049 P(node) =0.05125
## class counts: 20 21
## probabilities: 0.488 0.512
## left son=92 (27 obs) right son=93 (14 obs)
## Primary splits:
## DiscMM < 0.3 to the left, improve=1.736482, (0 missing)
## PctDiscMM < 0.1548655 to the left, improve=1.736482, (0 missing)
## PriceDiff < -0.085 to the right, improve=1.056432, (0 missing)
## ListPriceDiff < 0.155 to the right, improve=1.022196, (0 missing)
## PriceCH < 1.975 to the left, improve=1.009336, (0 missing)
## Surrogate splits:
## PctDiscMM < 0.1548655 to the left, agree=1.000, adj=1.000, (0 split)
## PriceDiff < -0.085 to the right, agree=0.927, adj=0.786, (0 split)
## SalePriceMM < 1.64 to the right, agree=0.854, adj=0.571, (0 split)
## WeekofPurchase < 270.5 to the left, agree=0.829, adj=0.500, (0 split)
## SpecialMM < 0.5 to the left, agree=0.780, adj=0.357, (0 split)
##
## Node number 47: 29 observations, complexity param=0.003246753
## predicted class=MM expected loss=0.2758621 P(node) =0.03625
## class counts: 8 21
## probabilities: 0.276 0.724
## left son=94 (13 obs) right son=95 (16 obs)
## Primary splits:
## StoreID < 2.5 to the right, improve=3.2496680, (0 missing)
## STORE < 2.5 to the right, improve=1.6121810, (0 missing)
## DiscMM < 0.1 to the left, improve=0.9441016, (0 missing)
## PctDiscMM < 0.047847 to the left, improve=0.9441016, (0 missing)
## WeekofPurchase < 248.5 to the right, improve=0.7417625, (0 missing)
## Surrogate splits:
## STORE < 2.5 to the right, agree=0.793, adj=0.538, (0 split)
## Store7Yes < 0.5 to the right, agree=0.759, adj=0.462, (0 split)
## LoyalCH < 0.51 to the right, agree=0.690, adj=0.308, (0 split)
## PriceCH < 1.975 to the right, agree=0.655, adj=0.231, (0 split)
## SalePriceMM < 1.74 to the right, agree=0.655, adj=0.231, (0 split)
##
## Node number 50: 7 observations
## predicted class=CH expected loss=0.2857143 P(node) =0.00875
## class counts: 5 2
## probabilities: 0.714 0.286
##
## Node number 51: 24 observations
## predicted class=MM expected loss=0.3333333 P(node) =0.03
## class counts: 8 16
## probabilities: 0.333 0.667
##
## Node number 86: 17 observations
## predicted class=CH expected loss=0.3529412 P(node) =0.02125
## class counts: 11 6
## probabilities: 0.647 0.353
##
## Node number 87: 7 observations
## predicted class=MM expected loss=0.2857143 P(node) =0.00875
## class counts: 2 5
## probabilities: 0.286 0.714
##
## Node number 92: 27 observations, complexity param=0.003246753
## predicted class=CH expected loss=0.4074074 P(node) =0.03375
## class counts: 16 11
## probabilities: 0.593 0.407
## left son=184 (8 obs) right son=185 (19 obs)
## Primary splits:
## ListPriceDiff < 0.115 to the right, improve=1.813353, (0 missing)
## StoreID < 2.5 to the left, improve=1.366449, (0 missing)
## STORE < 2.5 to the left, improve=1.337037, (0 missing)
## PriceCH < 1.875 to the left, improve=1.070370, (0 missing)
## SalePriceCH < 1.875 to the left, improve=1.070370, (0 missing)
## Surrogate splits:
## StoreID < 2.5 to the left, agree=0.852, adj=0.500, (0 split)
## PriceMM < 2.155 to the right, agree=0.778, adj=0.250, (0 split)
## SalePriceMM < 2.155 to the right, agree=0.778, adj=0.250, (0 split)
## WeekofPurchase < 273 to the right, agree=0.741, adj=0.125, (0 split)
## STORE < 2.5 to the left, agree=0.741, adj=0.125, (0 split)
##
## Node number 93: 14 observations
## predicted class=MM expected loss=0.2857143 P(node) =0.0175
## class counts: 4 10
## probabilities: 0.286 0.714
##
## Node number 94: 13 observations
## predicted class=CH expected loss=0.4615385 P(node) =0.01625
## class counts: 7 6
## probabilities: 0.538 0.462
##
## Node number 95: 16 observations
## predicted class=MM expected loss=0.0625 P(node) =0.02
## class counts: 1 15
## probabilities: 0.062 0.938
##
## Node number 184: 8 observations
## predicted class=CH expected loss=0.125 P(node) =0.01
## class counts: 7 1
## probabilities: 0.875 0.125
##
## Node number 185: 19 observations
## predicted class=MM expected loss=0.4736842 P(node) =0.02375
## class counts: 9 10
## probabilities: 0.474 0.526- Predict the response on the test data, and produce a confusion matrix comparing the test labels to the predicted test labels. What is the test error rate?
test_pred <- predict(tree_fit, OJ_test)
cm <- confusionMatrix(test_pred, OJ_test$Purchase)
print(cm)## Confusion Matrix and Statistics
##
## Reference
## Prediction CH MM
## CH 135 29
## MM 26 80
##
## Accuracy : 0.7963
## 95% CI : (0.7433, 0.8427)
## No Information Rate : 0.5963
## P-Value [Acc > NIR] : 2.055e-12
##
## Kappa : 0.575
##
## Mcnemar's Test P-Value : 0.7874
##
## Sensitivity : 0.8385
## Specificity : 0.7339
## Pos Pred Value : 0.8232
## Neg Pred Value : 0.7547
## Prevalence : 0.5963
## Detection Rate : 0.5000
## Detection Prevalence : 0.6074
## Balanced Accuracy : 0.7862
##
## 'Positive' Class : CH
## test_err <- mean(test_pred != OJ_test$Purchase)
print(test_err)## [1] 0.2037037- Use cross-validation on the training set in order to determine the optimal tree size.
set.seed(42)
cv_tree <- rpart(Purchase ~ ., data = OJ_train,
method = "class",
control = rpart.control(cp = 0.0001, xval = 10))
cp_table <- cv_tree$cptable
print(cp_table)## CP nsplit rel error xerror xstd
## 1 0.5292207792 0 1.0000000 1.0000000 0.04468505
## 2 0.0151515152 1 0.4707792 0.5064935 0.03638392
## 3 0.0086580087 4 0.4253247 0.5194805 0.03673282
## 4 0.0081168831 9 0.3798701 0.5259740 0.03690389
## 5 0.0032467532 11 0.3636364 0.5292208 0.03698859
## 6 0.0006493506 17 0.3441558 0.5097403 0.03647200
## 7 0.0001000000 22 0.3409091 0.5357143 0.03715636- Produce a plot with tree size on the x-axis and cross-validated classification error rate on the y-axis.
tree_size <- cp_table[, "nsplit"] + 1
cv_error <- cp_table[, "xerror"]
plot(tree_size, cv_error, type = "b",
xlab = "Tree Size (terminal nodes)",
ylab = "CV Classification Error",
main = "CV Error vs Tree Size")
plotcp(cv_tree)
- Which tree size corresponds to the lowest cross-validated classification error rate?
best_size <- tree_size[which.min(cv_error)]
best_cp <- cp_table[which.min(cv_error), "CP"]
print(best_size)## 2
## 2print(best_cp)## [1] 0.01515152- Produce a pruned tree corresponding to the optimal tree size obtained using cross-validation. If cross-validation does not lead to selection of a pruned tree, then create a pruned tree with five terminal nodes.
if (best_size > 1) {
pruned_tree <- prune(cv_tree, cp = best_cp)
} else {
target_row <- cp_table[cp_table[, "nsplit"] == 4, , drop = FALSE]
fallback_cp <- target_row[1, "CP"]
pruned_tree <- prune(cv_tree, cp = fallback_cp)
}
rpart.plot(pruned_tree, extra = 104, fallen.leaves = TRUE)
n_terminal_pruned <- sum(pruned_tree$frame$var == "<leaf>")
print(n_terminal_pruned)## [1] 2- Compare the training error rates between the pruned and unpruned trees. Which is higher?
pruned_train_pred <- predict(pruned_tree, OJ_train, type = "class")
pruned_train_err <- mean(pruned_train_pred != OJ_train$Purchase)
print(pruned_train_pred)## 561 321 634 49 24 356 165 622 410 899 601 932 997 621 860 259
## CH CH CH CH CH MM CH CH MM CH CH CH CH CH CH CH
## 481 1066 299 406 314 836 982 146 197 226 504 984 727 945 922 626
## CH CH MM MM CH CH CH CH CH MM CH CH MM MM CH CH
## 262 390 130 1027 374 770 1015 698 650 40 517 33 1041 103 228 109
## MM MM CH CH CH CH CH MM CH CH CH CH MM CH MM CH
## 1002 329 669 76 980 777 491 547 733 16 357 732 248 1006 325 988
## MM CH MM CH MM CH CH MM MM CH MM MM CH MM MM CH
## 630 642 82 920 881 914 1008 1063 360 951 296 149 569 100 298 402
## MM CH CH MM CH CH MM MM CH MM MM MM CH CH CH MM
## 91 781 181 54 851 288 720 758 60 285 849 620 969 377 853 638
## CH CH CH CH CH MM MM CH CH MM CH CH MM MM CH CH
## 427 442 112 584 981 1058 934 513 141 718 901 311 912 474 811 554
## MM CH CH CH MM MM CH CH CH MM CH MM MM MM CH MM
## 42 760 865 251 441 1020 25 883 703 544 1018 238 526 623 1038 1044
## CH CH MM CH CH CH CH CH MM MM CH CH MM CH CH CH
## 1052 446 933 1043 369 512 983 938 754 799 930 862 224 774 214 294
## CH CH CH CH MM CH CH MM MM CH MM CH MM MM CH MM
## 607 518 852 764 783 546 426 471 188 254 268 640 1062 41 193 578
## CH CH CH CH CH MM CH CH CH CH CH MM CH CH CH CH
## 824 664 98 537 348 107 317 14 162 636 706 926 949 697 796 1009
## CH CH CH CH CH CH CH CH CH CH MM MM MM MM MM MM
## 37 138 935 773 1032 78 946 668 97 741 483 182 961 127 940 493
## CH CH MM MM CH CH MM MM MM MM CH CH MM CH MM CH
## 555 692 506 337 539 542 180 868 212 587 201 401 62 269 382 124
## MM MM CH MM MM CH CH CH CH CH CH MM CH MM MM CH
## 63 1070 573 628 769 540 2 671 648 1022 208 771 885 956 12 705
## CH CH MM MM CH CH CH CH CH CH CH MM CH MM CH MM
## 670 563 444 677 559 910 198 10 255 871 745 515 1007 751 284 923
## CH CH CH CH CH MM CH CH CH CH CH CH MM CH MM CH
## 463 605 313 84 464 225 1056 102 171 489 662 694 567 566 685 421
## CH CH CH CH CH MM MM CH CH CH CH MM MM MM MM MM
## 878 207 85 153 240 1067 139 156 274 818 1045 762 170 292 148 719
## CH CH CH CH CH CH CH CH MM CH CH CH CH MM MM MM
## 189 113 27 606 645 86 1039 250 169 1011 550 362 457 115 779 789
## CH CH CH CH CH CH MM CH CH CH MM MM CH CH CH CH
## 213 801 1003 928 438 625 873 699 469 842 105 202 88 370 391 398
## CH MM MM MM MM CH CH MM CH MM CH CH CH MM MM MM
## 916 693 522 121 1060 894 900 163 418 46 287 826 376 280 404 715
## CH MM CH CH CH CH CH CH MM CH MM CH MM MM MM MM
## 825 379 206 906 829 301 358 684 647 159 653 378 776 987 514 857
## CH MM CH MM CH MM CH MM CH CH CH MM CH CH CH CH
## 387 1026 870 265 893 711 627 594 409 979 986 73 659 335 757 247
## MM CH CH CH CH MM CH CH MM MM CH CH CH MM MM CH
## 131 150 61 20 682 354 529 1004 211 174 273 94 330 429 690 179
## CH MM CH CH MM CH CH MM CH CH MM CH MM MM MM CH
## 74 304 473 346 231 366 116 108 722 326 803 738 618 1025 345 258
## CH MM MM CH CH MM CH CH MM MM CH MM CH CH CH CH
## 393 184 1037 1046 654 192 891 962 425 809 460 22 977 132 579 187
## MM CH MM CH CH CH CH MM MM CH MM CH MM CH CH CH
## 53 637 59 752 902 87 1024 994 660 874 709 820 3 1061 991 730
## CH CH CH MM CH CH CH MM CH CH MM CH CH CH CH CH
## 1054 596 475 168 665 496 218 332 724 110 119 619 737 663 896 804
## CH CH MM CH CH CH CH MM MM CH CH CH MM MM CH CH
## 592 794 527 23 904 339 966 574 267 365 586 123 879 875 367 993
## CH MM CH CH CH MM MM MM CH MM CH CH CH CH MM CH
## 458 603 1040 943 281 511 536 975 528 658 1059 995 195 831 341 1049
## CH CH MM MM MM CH CH MM CH CH CH MM CH CH CH CH
## 802 375 408 643 158 227 959 908 423 782 309 974 26 886 117 678
## CH MM MM CH CH CH MM MM MM CH MM MM CH CH CH CH
## 252 844 466 812 1035 104 767 1036 657 256 126 890 807 557 144 755
## CH MM CH CH CH CH CH CH CH MM CH CH CH MM MM MM
## 237 136 249 503 823 95 581 233 609 749 918 331 161 784 271 68
## CH CH CH CH CH CH CH CH CH MM CH CH CH MM MM CH
## 1016 655 223 355 827 120 8 772 176 632 689 530 608 133 543 312
## CH CH MM CH CH CH CH MM CH CH MM CH CH CH CH CH
## 532 548 264 275 114 266 813 766 759 32 490 936 488 461 519 203
## CH MM CH MM CH CH CH CH MM CH CH MM CH MM CH CH
## 11 143 761 971 485 568 775 412 708 39 531 204 222 534 800 882
## CH CH MM MM CH MM MM MM MM MM CH CH MM CH MM CH
## 700 552 276 911 439 897 593 816 939 921 1010 498 571 599 318 69
## MM MM MM CH CH CH CH CH MM CH CH MM MM CH CH CH
## 780 535 1055 739 18 242 178 431 449 392 785 30 937 307 666 448
## CH CH CH MM MM CH CH MM CH MM MM CH MM MM MM CH
## 277 872 83 125 235 729 1029 753 494 157 516 278 388 215 867 236
## MM CH CH CH CH CH CH CH CH CH CH MM MM CH CH CH
## 746 482 950 295 9 319 190 19 21 363 447 713 372 768 177 324
## CH CH MM MM CH CH CH MM CH MM CH MM MM CH CH MM
## 847 484 1069 92 1017 420 185 468 155 154 57 597 232 291 186 13
## MM CH CH CH CH MM CH CH CH CH CH CH CH MM CH CH
## 497 909 297 595 747 394 352 953 915 353 521 65 889 383 244 58
## MM MM MM CH CH MM CH MM CH CH CH CH CH MM CH CH
## 245 28 985 361 602 371 1064 414 451 152 172 34 652 832 701 691
## CH CH CH CH CH CH MM MM MM MM CH CH CH MM MM MM
## 717 437 843 725 351 998 884 72 415 166 99 589 175 4 913 815
## MM MM MM MM CH CH MM CH MM CH CH CH CH MM CH CH
## 840 508 137 443 405 523 895 210 453 147 1034 892 996 821 750 963
## MM CH CH CH MM CH CH CH CH MM CH CH MM CH CH CH
## 389 403 947 229 1 350 436 624 316 196 71 142 839 495 344 505
## MM MM MM MM CH CH MM CH CH CH CH CH MM CH CH CH
## 545 478 931 726 35 492 837 582 990 970 219 992 17 833 1019 1033
## MM CH MM MM CH CH MM CH CH MM CH MM CH MM CH CH
## 1001 861 676 972 562 106 135 952 1053 838 322 989 735 748 145 432
## MM CH CH MM MM CH CH MM CH MM CH CH MM MM MM MM
## 241 320 80 477 327 610 814 56 667 183 364 67 164 433 1028 564
## CH CH CH CH MM CH CH CH MM CH CH CH CH CH CH CH
## 500 293 501 848 111 380 721 828 965 397 954 631 612 79 342 45
## MM MM MM MM CH MM MM CH CH MM MM CH MM CH CH CH
## 373 66 604 551 253 672 859 510 866 101 588 359 960 167 903 716
## MM CH CH MM CH CH CH CH MM CH CH MM MM CH CH MM
## Levels: CH MMprint(pruned_train_err)## [1] 0.18125- Compare the test error rates between the pruned and unpruned trees. Which is higher?
pruned_test_pred <- predict(pruned_tree, OJ_test, type = "class")
pruned_test_err <- mean(pruned_test_pred != OJ_test$Purchase)
print(pruned_train_pred)## 561 321 634 49 24 356 165 622 410 899 601 932 997 621 860 259
## CH CH CH CH CH MM CH CH MM CH CH CH CH CH CH CH
## 481 1066 299 406 314 836 982 146 197 226 504 984 727 945 922 626
## CH CH MM MM CH CH CH CH CH MM CH CH MM MM CH CH
## 262 390 130 1027 374 770 1015 698 650 40 517 33 1041 103 228 109
## MM MM CH CH CH CH CH MM CH CH CH CH MM CH MM CH
## 1002 329 669 76 980 777 491 547 733 16 357 732 248 1006 325 988
## MM CH MM CH MM CH CH MM MM CH MM MM CH MM MM CH
## 630 642 82 920 881 914 1008 1063 360 951 296 149 569 100 298 402
## MM CH CH MM CH CH MM MM CH MM MM MM CH CH CH MM
## 91 781 181 54 851 288 720 758 60 285 849 620 969 377 853 638
## CH CH CH CH CH MM MM CH CH MM CH CH MM MM CH CH
## 427 442 112 584 981 1058 934 513 141 718 901 311 912 474 811 554
## MM CH CH CH MM MM CH CH CH MM CH MM MM MM CH MM
## 42 760 865 251 441 1020 25 883 703 544 1018 238 526 623 1038 1044
## CH CH MM CH CH CH CH CH MM MM CH CH MM CH CH CH
## 1052 446 933 1043 369 512 983 938 754 799 930 862 224 774 214 294
## CH CH CH CH MM CH CH MM MM CH MM CH MM MM CH MM
## 607 518 852 764 783 546 426 471 188 254 268 640 1062 41 193 578
## CH CH CH CH CH MM CH CH CH CH CH MM CH CH CH CH
## 824 664 98 537 348 107 317 14 162 636 706 926 949 697 796 1009
## CH CH CH CH CH CH CH CH CH CH MM MM MM MM MM MM
## 37 138 935 773 1032 78 946 668 97 741 483 182 961 127 940 493
## CH CH MM MM CH CH MM MM MM MM CH CH MM CH MM CH
## 555 692 506 337 539 542 180 868 212 587 201 401 62 269 382 124
## MM MM CH MM MM CH CH CH CH CH CH MM CH MM MM CH
## 63 1070 573 628 769 540 2 671 648 1022 208 771 885 956 12 705
## CH CH MM MM CH CH CH CH CH CH CH MM CH MM CH MM
## 670 563 444 677 559 910 198 10 255 871 745 515 1007 751 284 923
## CH CH CH CH CH MM CH CH CH CH CH CH MM CH MM CH
## 463 605 313 84 464 225 1056 102 171 489 662 694 567 566 685 421
## CH CH CH CH CH MM MM CH CH CH CH MM MM MM MM MM
## 878 207 85 153 240 1067 139 156 274 818 1045 762 170 292 148 719
## CH CH CH CH CH CH CH CH MM CH CH CH CH MM MM MM
## 189 113 27 606 645 86 1039 250 169 1011 550 362 457 115 779 789
## CH CH CH CH CH CH MM CH CH CH MM MM CH CH CH CH
## 213 801 1003 928 438 625 873 699 469 842 105 202 88 370 391 398
## CH MM MM MM MM CH CH MM CH MM CH CH CH MM MM MM
## 916 693 522 121 1060 894 900 163 418 46 287 826 376 280 404 715
## CH MM CH CH CH CH CH CH MM CH MM CH MM MM MM MM
## 825 379 206 906 829 301 358 684 647 159 653 378 776 987 514 857
## CH MM CH MM CH MM CH MM CH CH CH MM CH CH CH CH
## 387 1026 870 265 893 711 627 594 409 979 986 73 659 335 757 247
## MM CH CH CH CH MM CH CH MM MM CH CH CH MM MM CH
## 131 150 61 20 682 354 529 1004 211 174 273 94 330 429 690 179
## CH MM CH CH MM CH CH MM CH CH MM CH MM MM MM CH
## 74 304 473 346 231 366 116 108 722 326 803 738 618 1025 345 258
## CH MM MM CH CH MM CH CH MM MM CH MM CH CH CH CH
## 393 184 1037 1046 654 192 891 962 425 809 460 22 977 132 579 187
## MM CH MM CH CH CH CH MM MM CH MM CH MM CH CH CH
## 53 637 59 752 902 87 1024 994 660 874 709 820 3 1061 991 730
## CH CH CH MM CH CH CH MM CH CH MM CH CH CH CH CH
## 1054 596 475 168 665 496 218 332 724 110 119 619 737 663 896 804
## CH CH MM CH CH CH CH MM MM CH CH CH MM MM CH CH
## 592 794 527 23 904 339 966 574 267 365 586 123 879 875 367 993
## CH MM CH CH CH MM MM MM CH MM CH CH CH CH MM CH
## 458 603 1040 943 281 511 536 975 528 658 1059 995 195 831 341 1049
## CH CH MM MM MM CH CH MM CH CH CH MM CH CH CH CH
## 802 375 408 643 158 227 959 908 423 782 309 974 26 886 117 678
## CH MM MM CH CH CH MM MM MM CH MM MM CH CH CH CH
## 252 844 466 812 1035 104 767 1036 657 256 126 890 807 557 144 755
## CH MM CH CH CH CH CH CH CH MM CH CH CH MM MM MM
## 237 136 249 503 823 95 581 233 609 749 918 331 161 784 271 68
## CH CH CH CH CH CH CH CH CH MM CH CH CH MM MM CH
## 1016 655 223 355 827 120 8 772 176 632 689 530 608 133 543 312
## CH CH MM CH CH CH CH MM CH CH MM CH CH CH CH CH
## 532 548 264 275 114 266 813 766 759 32 490 936 488 461 519 203
## CH MM CH MM CH CH CH CH MM CH CH MM CH MM CH CH
## 11 143 761 971 485 568 775 412 708 39 531 204 222 534 800 882
## CH CH MM MM CH MM MM MM MM MM CH CH MM CH MM CH
## 700 552 276 911 439 897 593 816 939 921 1010 498 571 599 318 69
## MM MM MM CH CH CH CH CH MM CH CH MM MM CH CH CH
## 780 535 1055 739 18 242 178 431 449 392 785 30 937 307 666 448
## CH CH CH MM MM CH CH MM CH MM MM CH MM MM MM CH
## 277 872 83 125 235 729 1029 753 494 157 516 278 388 215 867 236
## MM CH CH CH CH CH CH CH CH CH CH MM MM CH CH CH
## 746 482 950 295 9 319 190 19 21 363 447 713 372 768 177 324
## CH CH MM MM CH CH CH MM CH MM CH MM MM CH CH MM
## 847 484 1069 92 1017 420 185 468 155 154 57 597 232 291 186 13
## MM CH CH CH CH MM CH CH CH CH CH CH CH MM CH CH
## 497 909 297 595 747 394 352 953 915 353 521 65 889 383 244 58
## MM MM MM CH CH MM CH MM CH CH CH CH CH MM CH CH
## 245 28 985 361 602 371 1064 414 451 152 172 34 652 832 701 691
## CH CH CH CH CH CH MM MM MM MM CH CH CH MM MM MM
## 717 437 843 725 351 998 884 72 415 166 99 589 175 4 913 815
## MM MM MM MM CH CH MM CH MM CH CH CH CH MM CH CH
## 840 508 137 443 405 523 895 210 453 147 1034 892 996 821 750 963
## MM CH CH CH MM CH CH CH CH MM CH CH MM CH CH CH
## 389 403 947 229 1 350 436 624 316 196 71 142 839 495 344 505
## MM MM MM MM CH CH MM CH CH CH CH CH MM CH CH CH
## 545 478 931 726 35 492 837 582 990 970 219 992 17 833 1019 1033
## MM CH MM MM CH CH MM CH CH MM CH MM CH MM CH CH
## 1001 861 676 972 562 106 135 952 1053 838 322 989 735 748 145 432
## MM CH CH MM MM CH CH MM CH MM CH CH MM MM MM MM
## 241 320 80 477 327 610 814 56 667 183 364 67 164 433 1028 564
## CH CH CH CH MM CH CH CH MM CH CH CH CH CH CH CH
## 500 293 501 848 111 380 721 828 965 397 954 631 612 79 342 45
## MM MM MM MM CH MM MM CH CH MM MM CH MM CH CH CH
## 373 66 604 551 253 672 859 510 866 101 588 359 960 167 903 716
## MM CH CH MM CH CH CH CH MM CH CH MM MM CH CH MM
## Levels: CH MMprint(pruned_train_err)## [1] 0.18125