tests/testthat/test-multipleimputation.R

In NumbersInternational/flipRegression: Estimates standard regression models

context("Multiple imputation")

data("bank", package = "flipExampleData")
zbank <- bank[1:200,]
set.seed(23442)
zbank$rnd <- runif(nrow(zbank))
zbank$rnd1 <- runif(nrow(zbank))
zbank$rnd2 <- runif(nrow(zbank))
zbank$rnd3 <- runif(nrow(zbank))
zbank$rnd4 <- runif(nrow(zbank))
attr(bank$Overall, "label") <- "Overall satisfaction"
attr(bank$Fees, "label") <- "Fees paid"
attr(bank$Online, "label") <- "Online banking"

data("cola", package = "flipExampleData")
cola <- cola[1:150,]
cola$Q3[1:100] <- NA
cola$Q3 <- unclass(cola$Q3)

test_that("Multiple imputation with auxiliary variables ", {
    # No auxiliary variables, data has an argument
    z1 = Regression(Overall ~ Branch + Interest, data = zbank, missing = "Multiple imputation")$coef[2]
    # No auxiliary variables, data inferred from environment
    attach(zbank)
    z2 = Regression(Overall ~ Branch + Interest, missing = "Multiple imputation")$coef[2]
    detach(zbank)
    expect_equal(z1, z2)
    # Auxiliary variables, data has an argument
    zaux <- data.frame(a = zbank$Phone, b = zbank$Online)
    z3 = Regression(Overall ~ Branch + Interest,auxiliary.data = zaux, data = zbank, missing = "Multiple imputation")$coef[2]
    # Auxiliary variables, data inferred from environment
    attach(zbank)
    z4 = Regression(Overall ~ Branch + Interest, auxiliary.data = zaux, missing = "Multiple imputation")$coef[2]
    detach(zbank)
    expect_false(isTRUE(all.equal(z1, z4)))
    # Auxiliary variables, incorrect number of rows.
    zaux <- data.frame(a = zbank$Phone, b = zbank$Online)[1:10,]
    expect_error(Regression(Overall ~ Branch + Interest,auxiliary.data = zaux, data = zbank, missing = "Multiple imputation"))

})


test_that("Multiple imputation run using Regression", {
    est <- flipData::EstimationData(Overall ~ Fees + Interest + Phone + Branch + Online + ATM + rnd + rnd1 + rnd2 + rnd3 + rnd4, zbank, missing = "Multiple imputation", m = 10)
    models <- lapply(est$estimation.data, FUN = function(x) Regression(Overall ~ Fees + Interest + Phone + Branch + Online + ATM + rnd + rnd1 + rnd2 + rnd3 + rnd4, data = x))
    expect_error(MultipleImputationCoefficientTable(models), NA)
    #expect_equal(coefs[12,5], 0.211, 0.001)
})

test_that("Multiple imputation ", {
    expect_error(z <- Regression(Overall ~ Fees + Interest + Phone + Branch + Online + ATM + rnd + rnd1 + rnd2 + rnd3 + rnd4,
                                data = zbank, missing = "Multiple imputation"),
                 NA)
    #expect_equal(z$coefficient.table[12,5], 0.187, 0.001)
})

# Using examples from https://www.ssc.wisc.edu/sscc/pubs/mi/missmech.do

test_that("Other examples",
{
    #  generate data
    set.seed(88)
    n <- 1000
    X <- rnorm(n)
    y <- X + rnorm(n)

    # drop values of x
    # probability of x being missing 10%
    # data is MCAR
    x <- X
    x[runif(n) < .1] <- NA

    expect_error(Regression(y ~ x, data = data.frame(y = y, x = x)), NA)
    expect_error(Regression(y ~ x, data = data.frame(y = y, x = x), missing = "Multiple imputation", m = 10), NA)

    # drop values of x
    # probability of x being missing depends on y (observed)
    # data is MAR
    x <- X
    x[runif(n) < y] <- NA
    expect_error(Regression(y ~ x, data = data.frame(y = y, x = x)), NA)
    expect_error(Regression(y ~ x, data = data.frame(y = y, x = x), missing = "Multiple imputation"), NA)


    # drop values of x
    # probability of x being missing now depends on x (sometimes unobserved)
    # data is MNAR
    x <- X
    x[X < runif(n)] <- NA
    z <- runif(n)
    # Prevent pop-ups
    mockery::stub(print.Regression, "print.htmlwidget", NULL)
    suppressWarnings(Regression(y ~ x + z, data = data.frame(y = y, x = x, z = z)))
    expect_error(Regression(y ~ x + z, data = data.frame(y = y, x = x, z = z), missing = "Multiple imputation"), NA)
    expect_error(Regression(y ~ x + z, data = data.frame(y = y, x = x, z = z), missing = "Use partial data (pairwise correlations)"), NA)


    # Case study

    distance <- Distance <- c(5, 5, 10, 10, 15, 15, 20, 20)
    price <- Price <- c(1.6, 2.4, 1.1, 1.9, .6, 1.4, .1, .9)

    # Suppress output but test plot works
    pdf(file = tempfile(fileext = ".pdf"))
    expect_error(PredictionPlot(Regression(price ~ distance)), NA)
    dev.off()

    ## M ~ X
    distance <- Distance
    distance[7:8] <- NA

    # Complete case
    expect_error(Regression(price ~ distance, data = data.frame(distance, price)), NA)

    expect_error(Regression(price ~ distance, data = data.frame(distance, price), missing = "Use partial data (pairwise correlations)"), NA)
    expect_error(Regression(price ~ distance, data = data.frame(distance, price)[1:6, ], missing = "Use partial data (pairwise correlations)"), NA)

    # Regression-based imputation
    expect_error(Regression(price ~ distance, data = data.frame(distance, price), missing = "Multiple imputation"), NA)

    # Hot decking
    distance[7:8] <- 15
    expect_error(Regression(price ~ distance, data = data.frame(distance, price)), NA)

    # Mean imputation
    distance[7:8] <- mean(distance[1:6])
    expect_error(Regression(price ~ distance, data = data.frame(distance, price)), NA)

    expect_error(predict(Regression(distance ~ price)), NA)

    # M ~ Y
    distance <- Distance
    distance[c(5,7)] <- NA
    expect_error(Regression(price ~ distance, data = data.frame(distance, price)), NA)
    expect_error(Regression(price ~ distance, data = data.frame(distance, price), missing = "Use partial data (pairwise correlations)"), NA)
    expect_error(Regression(price ~ distance, data = data.frame(distance, price), missing = "Multiple imputation"), NA)
})

df <- structure(list(Churn_cat = structure(c(1L, 1L, 2L, 1L, 2L, 2L,
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                                             1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L,
                                             2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
                                             1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
                                             2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
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                                             1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
                                             2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L,
                                             2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
                                             2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
                                             2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
                                             2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
                                             1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
                                             2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L,
                                             2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L,
                                             2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L,
                                             1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L,
                                             2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
                                             2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
                                             1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
                                             2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
                                             2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L,
                                             2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L,
                                             1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
                                             1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
                                             2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
                                             2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L,
                                             1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
                                             2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
                                             2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
                                             2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L,
                                             1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L,
                                             1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
                                             1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L,
                                             1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L,
                                             2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L,
                                             1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L,
                                             1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
                                             2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
                                             2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
                                             1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
                                             1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
                                             1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L,
                                             2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L,
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
                                             1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
                                             1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L,
                                             1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L,
                                             1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                             1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L), class = "factor", .Label = c("No",
                                                                                                                               "Yes"), questiontype = "PickOne", name = "Churn_cat", label = "Churn", question = "Churn"),
                     OnlineSecurity_cat = structure(c(1L, 3L, 3L, 3L, 1L, 1L,
                                                      1L, 3L, 1L, 3L, 3L, 2L, 1L, 1L, 3L, 3L, 2L, 3L, 1L, 1L, 1L,
                                                      2L, 2L, 1L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 3L,
                                                      1L, 1L, 1L, 1L, 1L, 3L, 2L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 1L,
                                                      3L, 3L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 1L,
                                                      1L, 1L, 2L, 3L, 1L, 2L, 3L, 2L, 3L, 3L, 1L, 3L, 3L, 2L, 1L,
                                                      3L, 1L, 1L, 2L, 1L, 3L, 2L, 2L, 1L, 1L, 1L, 3L, 3L, 1L, 3L,
                                                      3L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 2L, 3L,
                                                      3L, 1L, 1L, 1L, 3L, 3L, 3L, 2L, 1L, 1L, 2L, 1L, 3L, 2L, 3L,
                                                      1L, 2L, 2L, 3L, 1L, 3L, 1L, 1L, 1L, 2L, 3L, 2L, 2L, 1L, 3L,
                                                      3L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 2L, 1L,
                                                      1L, 2L, 3L, 2L, 3L, 3L, 1L, 1L, 2L, 2L, 1L, 3L, 1L, 2L, 3L,
                                                      1L, 1L, 1L, 2L, 2L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L,
                                                      1L, 1L, 2L, 1L, 3L, 1L, 2L, 3L, 2L, 3L, 2L, 1L, 1L, 2L, 3L,
                                                      1L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 2L, 2L, 1L, 3L,
                                                      3L, 3L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 3L, 3L, 1L, 1L, 3L, 3L,
                                                      3L, 3L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 3L,
                                                      1L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 3L, 3L, 1L, 3L, 1L,
                                                      1L, 1L, 3L, 3L, 3L, 2L, 3L, 2L, 2L, 1L, 3L, 1L, 1L, 1L, 1L,
                                                      1L, 3L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                                      3L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 2L,
                                                      1L, 1L, 1L, 3L, 2L, 3L, 3L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 3L,
                                                      1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
                                                      1L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 1L, 2L, 1L, 3L, 3L,
                                                      1L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 3L, 2L, 1L, 1L, 2L, 1L, 1L,
                                                      3L, 2L, 1L, 3L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 1L,
                                                      1L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 3L,
                                                      3L, 1L, 1L, 2L, 2L, 2L, 1L, 3L, 2L, 2L, 3L, 1L, 2L, 2L, 1L,
                                                      2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 3L, 1L,
                                                      1L, 1L, 1L, 3L, 2L, 3L, 3L, 1L, 2L, 1L, 2L, 3L, 1L, 1L, 3L,
                                                      3L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 3L, 2L, 3L, 1L, 1L, 2L, 1L,
                                                      1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 2L,
                                                      1L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 1L, 1L, 1L,
                                                      1L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 3L,
                                                      3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 2L, 3L, 3L, 1L, 1L, 3L, 1L,
                                                      3L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 2L, 1L, 2L,
                                                      2L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 1L,
                                                      1L, 1L, 3L, 2L, 3L, 3L, 2L, 2L, 1L, 3L, 2L, 3L, 1L, 1L, 1L,
                                                      2L, 3L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 3L,
                                                      3L, 1L, 3L, 2L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 2L, 3L, 3L, 3L,
                                                      2L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 3L, 3L,
                                                      3L, 1L, 3L, 3L, 1L, 3L, 2L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 1L,
                                                      3L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 2L, 3L, 1L,
                                                      1L, 3L, 3L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                                      1L, 2L, 2L, 2L, 1L, 3L, 3L, 2L, 2L, 1L, 1L, 2L, 3L, 2L, 1L,
                                                      1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 3L, 2L, 1L, 1L, 1L, 1L,
                                                      1L, 3L, 1L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 3L, 2L, 1L, 2L, 2L,
                                                      1L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 3L, 3L, 1L, 1L, 1L, 2L,
                                                      1L, 2L, 3L, 2L, 3L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
                                                      2L, 1L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 3L,
                                                      3L, 3L, 2L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 3L, 2L, 3L, 1L,
                                                      2L, 2L, 1L, 3L, 2L, 1L, 1L, 3L, 2L, 1L, 1L, 2L, 1L, 3L, 2L,
                                                      1L, 2L, 3L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 3L,
                                                      3L, 3L, 3L, 3L, 3L, 3L, 2L, 3L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
                                                      1L, 2L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 2L, 3L, 2L, 1L,
                                                      1L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 3L,
                                                      2L, 3L, 1L, 1L, 3L, 3L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L,
                                                      3L, 3L, 3L, 3L, 3L, 3L, 2L, 3L, 2L, 1L, 3L, 1L, 3L, 3L, 2L,
                                                      3L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 2L, 1L, 1L, 1L,
                                                      3L, 3L, 3L, 1L, 3L, 2L, 1L, 3L, 3L, 2L, 1L, 3L, 1L, 3L, 3L,
                                                      1L, 1L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 2L, 1L, 3L, 3L, 3L, 1L,
                                                      1L, 1L, 2L, 1L, 1L, 1L, 3L, 2L, 2L, 1L, 3L, 3L, 1L, 1L, 2L,
                                                      2L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L,
                                                      3L, 3L, 1L, 2L, 2L, 1L, 1L, 3L, 3L, 1L, 2L, 1L, 1L, 2L, 1L,
                                                      1L, 3L, 3L, 1L, 1L, 2L, 3L, 3L, 1L, 3L, 2L, 3L, 3L, 1L, 3L,
                                                      2L, 2L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 2L,
                                                      2L, 3L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 3L, 2L, 2L, 2L, 2L, 1L,
                                                      1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 2L, 3L,
                                                      3L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 2L, 3L, 3L, 1L, 1L, 1L, 3L,
                                                      1L, 3L, 1L, 3L, 1L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 1L, 3L, 1L,
                                                      2L, 1L, 1L, 3L, 1L, 3L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
                                                      1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 3L, 2L, 3L, 1L, 3L, 1L,
                                                      1L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
                                                      1L, 3L, 1L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 2L,
                                                      2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 3L, 3L, 3L, 1L, 1L, 1L,
                                                      2L, 1L, 3L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 2L, 1L, 2L,
                                                      3L, 1L, 2L, 3L, 3L, 2L, 2L, 3L, 2L, 3L, 2L, 1L, 1L, 1L, 3L,
                                                      3L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 3L,
                                                      1L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 1L, 3L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 3L,
                                                      3L, 1L, 1L, 1L, 1L, 3L, 2L, 2L, 3L, 1L, 1L, 1L, 2L, 1L, 1L,
                                                      1L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 3L,
                                                      1L, 3L, 1L, 1L, 1L, 2L, 3L, 3L, 3L, 1L, 3L, 1L, 2L, 3L, 1L,
                                                      1L, 2L, 1L, 1L, 2L, 3L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 1L,
                                                      1L, 2L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 3L, 1L, 1L, 1L, 3L,
                                                      3L, 1L, 3L, 3L, 2L, 3L, 2L, 3L, 3L, 3L, 3L, 2L, 3L, 2L, 3L,
                                                      2L, 1L, 3L, 2L, 1L, 1L, 1L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 3L,
                                                      1L, 1L, 3L, 1L, 1L, 3L, 3L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 1L,
                                                      1L, 3L, 1L, 1L, 2L, 2L, 2L, 3L, 2L, 3L, 3L, 2L, 2L, 2L, 1L,
                                                      3L, 1L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 1L, 1L, 2L, 2L, 1L, 3L,
                                                      1L, 2L, 3L, 2L, 1L, 1L, 2L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 2L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 2L,
                                                      1L, 1L, 2L, 3L, 2L, 1L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 1L, 3L,
                                                      1L, 2L, 1L, 1L, 3L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 3L, 2L, 2L,
                                                      1L, 1L, 1L, 2L, 1L, 2L, 3L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 3L,
                                                      1L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 2L,
                                                      1L, 2L, 3L, 1L, 3L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 3L, 1L,
                                                      1L, 1L, 2L, 2L, 2L, 3L, 3L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 1L,
                                                      3L, 2L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                                      2L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 1L, 3L, 3L, 1L,
                                                      2L, 1L, 3L, 2L, 3L, 2L, 3L, 1L, 1L, 1L, 2L, 3L, 1L, 1L, 1L,
                                                      3L, 2L, 1L, 1L, 3L, 2L, 1L, 1L, 2L, 1L, 1L, 3L, 2L, 3L, 2L,
                                                      3L, 3L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 3L,
                                                      3L, 1L, 1L, 3L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                                      2L, 1L, 1L, 2L, 3L, 1L, 3L, 1L, 2L, 3L, 1L, 3L, 1L, 1L, 1L,
                                                      1L, 1L, 1L, 1L, 2L, 2L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                                      1L, 3L, 1L, 1L, 3L, 3L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L,
                                                      1L, 3L, 2L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 3L,
                                                      3L, 1L, 2L, 3L, 2L, 2L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L,
                                                      3L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 2L,
                                                      3L, 2L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 2L, 2L, 1L,
                                                      3L, 2L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 3L, 1L, 1L,
                                                      3L, 3L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 1L,
                                                      1L, 2L, 2L, 3L, 3L, 2L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 2L, 2L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 2L,
                                                      1L, 2L, 2L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 3L, 3L, 1L,
                                                      1L, 1L, 2L, 1L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 3L, 2L,
                                                      3L, 1L, 2L, 1L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 1L,
                                                      2L, 1L, 1L, 3L, 3L, 2L, 3L, 1L, 1L, 3L, 1L, 1L, 2L, 3L, 3L,
                                                      2L, 1L, 2L, 3L, 2L, 1L, 1L, 1L, 2L, 3L, 1L, 3L, 2L, 1L, 1L,
                                                      3L, 3L, 2L, 3L, 1L, 1L, 2L, 2L, 3L, 1L, 1L, 3L, 3L, 2L, 3L,
                                                      2L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
                                                      1L, 1L, 1L, 2L, 1L, 1L, 3L, 2L, 1L, 2L, 3L, 1L, 3L, 1L, 1L,
                                                      1L, 2L, 1L, 2L, 3L, 2L, 3L, 2L, 3L, 1L, 2L, 2L, 2L, 1L, 3L,
                                                      1L, 1L, 1L, 1L, 2L, 3L, 3L, 3L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
                                                      3L, 1L, 1L, 2L, 1L, 3L, 2L, 3L, 3L, 3L, 1L, 3L, 2L, 1L, 1L,
                                                      3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 3L,
                                                      3L, 1L, 1L, 1L, 2L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 2L, 2L, 1L,
                                                      3L, 2L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
                                                      1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 3L, 2L, 3L, 2L, 2L, 2L, 3L,
                                                      1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L,
                                                      3L, 3L, 1L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 1L, 3L, 1L, 3L, 1L,
                                                      2L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 3L, 1L, 1L,
                                                      1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 1L,
                                                      2L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 3L, 2L, 1L, 1L,
                                                      1L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 3L, 1L, 2L, 2L, 3L, 3L,
                                                      1L, 1L, 2L, 3L, 3L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 2L, 1L,
                                                      1L, 3L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 3L, 1L, 3L, 3L, 1L, 3L,
                                                      1L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 3L, 3L, 1L, 2L, 2L, 3L, 1L,
                                                      1L, 1L, 3L, 3L, 3L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 1L,
                                                      2L, 3L, 2L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 1L,
                                                      3L, 1L, 1L, 2L, 2L, 2L, 3L, 1L, 3L, 3L, 1L, 3L, 1L, 2L, 2L,
                                                      2L, 1L, 1L, 1L, 3L, 1L, 3L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 3L,
                                                      1L, 2L, 3L, 1L, 1L, 2L, 3L, 1L, 1L, 1L, 3L, 2L, 2L, 1L, 1L,
                                                      2L, 1L, 1L, 2L, 1L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 1L, 3L, 2L,
                                                      3L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 2L, 3L, 2L, 2L, 1L,
                                                      1L, 1L, 1L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 1L, 3L, 2L, 1L, 2L,
                                                      2L, 1L, 1L, 2L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 2L, 1L,
                                                      3L, 2L, 2L, 1L, 3L, 3L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L,
                                                      3L, 2L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 3L,
                                                      2L, 2L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 2L, 3L, 3L, 3L,
                                                      3L, 1L, 3L, 2L, 1L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 2L, 1L, 1L,
                                                      1L, 1L, 2L, 3L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 3L, 3L,
                                                      1L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L,
                                                      1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 3L, 2L, 1L, 3L, 1L,
                                                      2L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                                      2L, 3L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 3L, 3L, 3L, 1L, 3L, 2L,
                                                      1L, 2L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 3L, 1L, 3L, 2L, 3L, 2L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 2L, 3L, 1L, 2L, 3L,
                                                      1L, 3L, 1L, 1L, 1L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 2L,
                                                      1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 2L, 3L, 3L, 1L,
                                                      1L, 1L, 2L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 3L,
                                                      1L, 1L, 2L, 3L, 2L, 1L, 1L, 1L, 3L, 3L, 1L, 2L, 3L, 2L, 1L,
                                                      3L, 3L, 3L, 2L, 2L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 1L, 3L,
                                                      3L, 1L, 1L, 2L, 1L, 2L, 1L, 3L, 2L, 2L, 2L, 3L, 1L, 1L, 1L,
                                                      2L, 1L, 1L, 2L, 2L, 1L, 3L, 2L, 1L, 3L, 3L, 3L, 1L, 3L, 1L,
                                                      2L, 1L, 3L, 2L, 1L, 1L, 3L, 1L, 3L, 1L, 2L, 3L, 1L, 1L, 2L,
                                                      2L, 2L, 1L, 3L, 3L, 2L, 2L, 2L, 3L, 2L, 2L, 2L, 1L, 2L, 1L,
                                                      3L, 3L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 2L, 3L,
                                                      2L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 3L, 2L, 3L, 1L, 2L, 3L,
                                                      3L, 1L, 3L, 3L, 3L, 3L, 3L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 3L,
                                                      3L, 1L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 3L, 1L, 2L, 2L, 1L,
                                                      1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 3L, 3L, 2L,
                                                      2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 1L, 3L, 1L,
                                                      1L, 1L, 3L, 1L, 2L, 3L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 3L,
                                                      1L, 2L, 2L, 1L, 3L, 1L, 1L, 3L, 1L, 3L, 3L, 2L, 3L, 1L, 3L,
                                                      1L, 1L, 3L, 1L, 2L, 3L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 2L,
                                                      1L, 2L, 3L, 2L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 2L, 3L, 3L,
                                                      3L, 1L, 3L, 3L, 3L, 1L, 3L, 2L, 3L, 3L, 1L, 2L, 3L, 2L, 2L,
                                                      2L, 1L, 2L, 1L, 3L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 1L,
                                                      3L, 3L, 2L, 2L, 3L, 3L, 3L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
                                                      1L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 2L, 1L, 3L, 3L, 3L, 1L,
                                                      1L, 2L, 2L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 1L,
                                                      1L, 1L, 3L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
                                                      1L, 3L, 1L, 3L, 2L, 2L, 3L, 2L, 2L, 2L, 1L, 1L, 3L, 3L, 1L,
                                                      3L, 1L, 2L, 2L, 1L, 3L, 3L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 3L,
                                                      1L, 3L, 3L, 1L, 1L, 3L, 2L, 3L, 1L, 3L, 3L, 1L, 3L, 3L, 1L,
                                                      3L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 3L, 3L, 2L, 3L, 1L, 1L,
                                                      2L, 1L, 2L, 3L, 1L, 3L, 2L, 3L, 3L, 2L, 1L, 3L, 2L, 2L, 2L,
                                                      1L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 1L, 2L, 2L, 2L, 3L,
                                                      1L, 3L, 2L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 3L, 1L, 3L, 2L,
                                                      1L, 1L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 1L,
                                                      1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 3L, 3L,
                                                      3L, 1L, 1L, 3L, 1L, 1L, 2L, 3L, 3L, 2L, 2L, 2L, 3L, 3L, 1L,
                                                      3L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 3L, 1L, 3L,
                                                      3L, 2L, 1L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 3L, 2L,
                                                      1L, 1L, 2L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 2L, 3L, 3L,
                                                      1L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 3L,
                                                      1L, 1L, 2L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 3L, 1L, 3L, 1L,
                                                      2L, 2L, 1L, 1L, 2L, 2L, 2L, 3L, 2L, 3L, 1L, 2L, 3L, 2L, 1L,
                                                      1L, 1L, 2L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 1L, 2L,
                                                      1L, 1L, 2L, 2L, 3L, 2L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 3L,
                                                      2L, 2L, 3L, 2L, 2L, 1L, 2L, 3L, 1L, 1L, 1L, 2L, 3L, 1L, 1L,
                                                      3L, 2L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                                      3L, 3L, 1L, 1L, 1L, 3L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                                      1L, 1L, 3L, 2L, 3L, 3L, 3L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 1L,
                                                      1L, 3L, 2L, 2L, 1L, 1L, 1L, 3L, 3L, 1L, 2L, 1L, 1L, 1L, 1L,
                                                      1L, 2L, 1L, 2L, 1L, 3L, 3L, 2L, 1L, 1L, 2L, 3L, 3L, 2L, 2L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 3L, 2L,
                                                      3L, 1L, 2L, 1L, 3L, 3L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
                                                      1L, 2L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 3L, 3L, 3L, 1L, 2L,
                                                      2L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 3L, 2L, 1L, 1L,
                                                      2L, 1L, 2L, 1L, 1L, 2L, 3L, 3L, 2L, 2L, 3L, 1L, 1L, 1L, 1L,
                                                      2L, 1L, 3L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L,
                                                      1L, 1L, 3L, 2L, 3L, 2L, 2L, 1L, 1L, 3L, 2L, 1L, 3L, 1L, 1L,
                                                      1L, 2L, 1L, 2L, 3L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 2L,
                                                      3L, 3L, 1L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 2L, 2L, 1L, 3L, 1L,
                                                      1L, 1L, 1L, 1L, 2L, 3L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L,
                                                      3L, 1L, 1L, 1L, 1L, 2L, 2L, 3L, 2L, 1L, 1L, 3L, 1L, 1L, 2L,
                                                      1L, 2L, 1L, 3L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 1L, 3L,
                                                      3L, 1L, 1L, 1L, 3L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 1L, 1L, 1L,
                                                      1L, 1L, 2L, 2L, 1L, 3L, 2L, 2L, 1L, 1L, 3L, 3L, 1L, 3L, 3L,
                                                      2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L,
                                                      2L, 1L, 1L, 3L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                                      1L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 3L, 1L, 3L, 2L,
                                                      1L, 3L, 1L, 3L, 3L, 2L, 1L, 1L, 3L, 2L, 2L, 2L, 3L, 2L, 1L,
                                                      3L, 2L, 1L, 1L, 1L, 3L, 2L, 3L, 1L, 2L, 2L, 1L, 1L, 3L, 3L,
                                                      3L, 3L, 3L, 1L, 1L, 2L, 1L, 2L, 3L, 3L, 2L, 2L, 1L, 3L, 1L,
                                                      1L, 3L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 3L, 3L, 3L, 3L, 1L, 1L,
                                                      1L, 1L, 3L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 2L, 1L, 1L, 1L, 3L,
                                                      3L, 1L, 3L, 3L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                                      3L, 2L, 1L, 2L, 1L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 2L, 1L, 3L,
                                                      2L, 1L, 1L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 1L,
                                                      3L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 2L, 1L,
                                                      3L, 3L, 1L, 2L, 1L, 3L, 2L, 3L, 1L, 1L, 2L, 2L, 2L, 3L, 3L,
                                                      1L, 3L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                                      2L, 1L, 2L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 3L, 3L, 3L, 1L, 1L,
                                                      3L, 3L, 3L, 3L, 1L, 1L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 2L, 1L,
                                                      1L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L,
                                                      2L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 2L,
                                                      3L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 2L, 1L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 1L,
                                                      1L, 3L, 1L, 1L, 2L, 1L, 2L, 3L, 2L, 2L, 3L, 1L, 1L, 3L, 2L,
                                                      2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L,
                                                      2L, 1L, 3L, 1L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 3L,
                                                      1L, 1L, 3L, 3L, 2L, 1L, 1L, 1L, 1L, 2L, 3L, 1L, 3L, 2L, 1L,
                                                      1L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 1L,
                                                      1L, 3L, 1L, 1L, 2L, 2L, 3L, 2L, 3L, 3L, 1L, 2L, 2L, 1L, 2L,
                                                      3L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 2L, 3L, 2L, 3L, 2L, 2L, 1L,
                                                      1L, 1L, 3L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 2L, 1L, 1L, 2L, 1L,
                                                      3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 1L, 2L, 1L,
                                                      1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 2L, 2L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 1L,
                                                      1L, 1L, 3L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 3L, 3L,
                                                      1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 3L, 2L, 1L, 3L, 1L,
                                                      3L, 2L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 2L, 2L, 2L, 2L, 1L, 1L,
                                                      3L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 1L,
                                                      1L, 2L, 1L, 3L, 3L, 2L, 2L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 1L,
                                                      1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L,
                                                      1L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 2L, 1L,
                                                      3L, 2L, 1L, 3L, 2L, 2L, 3L, 2L, 3L, 2L, 1L, 3L, 1L, 2L, 1L,
                                                      1L, 1L, 3L, 2L, 1L, 3L, 3L, 2L, 2L, 3L, 1L, 1L, 1L, 1L, 1L,
                                                      3L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 2L, 3L, 2L,
                                                      3L, 2L, 3L, 1L, 1L, 2L, 1L, 1L, 2L, 3L, 3L, 3L, 1L, 3L, 1L,
                                                      3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 1L,
                                                      3L, 2L, 2L, 1L, 3L, 2L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 2L, 1L,
                                                      1L, 2L, 1L, 2L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 3L, 3L, 1L, 3L,
                                                      2L, 1L, 3L, 1L, 1L, 1L, 3L, 2L, 3L, 2L, 2L, 2L, 1L, 3L, 2L,
                                                      2L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 1L, 3L, 2L, 2L, 2L, 1L, 1L,
                                                      3L, 1L, 3L, 3L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 2L, 2L, 1L, 3L,
                                                      3L, 1L, 3L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 3L,
                                                      1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 3L, 2L, 3L, 1L,
                                                      3L, 1L, 3L, 1L, 3L, 3L, 1L, 3L, 3L, 2L, 1L, 3L, 1L, 1L, 1L,
                                                      3L, 2L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 2L, 3L, 2L,
                                                      3L, 1L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 1L, 3L, 2L, 2L, 3L,
                                                      2L, 3L, 1L, 2L, 1L, 1L, 3L, 1L, 1L, 3L, 2L, 2L, 1L, 1L, 1L,
                                                      2L, 1L, 1L, 1L, 3L, 2L, 2L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 3L,
                                                      1L, 2L, 2L, 1L, 1L, 1L, 3L, 2L, 1L, 3L, 2L, 1L, 2L, 3L, 3L,
                                                      1L, 3L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 3L, 2L, 2L, 1L, 1L, 2L,
                                                      2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 3L, 3L,
                                                      1L, 2L, 2L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 2L, 2L, 2L, 1L, 3L,
                                                      3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 2L,
                                                      2L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, 3L, 3L, 3L, 1L, 3L, 2L, 3L,
                                                      2L, 1L, 2L, 1L, 1L, 3L, 2L, 3L, 2L, 2L, 3L, 3L, 1L, 1L, 3L,
                                                      3L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 1L, 3L, 3L, 1L, 1L,
                                                      3L, 3L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
                                                      3L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 3L,
                                                      3L, 3L, 1L, 3L, 2L, 2L, 3L, 2L, 2L, 2L, 3L, 1L, 1L, 1L, 3L,
                                                      1L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 3L, 2L, 1L, 1L, 1L, 3L, 2L,
                                                      1L, 1L, 1L, 3L, 1L, 2L, 3L, 3L, 3L, 1L, 3L, 1L, 1L, 1L, 1L,
                                                      1L, 3L, 1L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 1L,
                                                      2L, 2L, 1L, 1L, 3L, 3L, 2L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 3L,
                                                      2L, 2L, 2L, 2L, 3L, 3L, 1L, 2L, 1L, 2L, 1L, 1L, 3L, 1L, 2L,
                                                      3L, 2L, 2L, 3L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 1L,
                                                      3L, 3L, 1L, 1L, 1L, 3L, 2L, 3L, 3L, 1L, 3L, 2L, 1L, 2L, 3L,
                                                      1L, 1L, 3L, 2L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 3L,
                                                      1L, 3L, 1L, 3L, 1L, 3L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 3L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 2L, 3L, 1L, 1L, 1L,
                                                      1L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 1L, 1L, 2L,
                                                      2L, 3L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 2L, 3L, 1L, 3L,
                                                      2L, 2L, 2L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 2L, 1L, 3L, 2L, 2L,
                                                      1L, 3L, 2L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 2L,
                                                      3L, 2L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                                      1L, 1L, 1L, 3L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 2L,
                                                      1L, 2L, 3L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 2L, 3L,
                                                      1L, 1L, 1L, 3L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 3L, 1L, 1L, 2L,
                                                      2L, 3L, 3L, 3L, 1L, 3L, 1L, 1L, 2L, 3L, 2L, 2L, 2L, 1L, 1L,
                                                      1L, 1L, 3L, 1L, 3L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 1L, 1L, 3L,
                                                      2L, 1L, 1L, 2L, 3L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L,
                                                      1L, 3L, 3L, 2L, 3L, 1L, 2L, 2L, 2L, 2L, 2L, 3L, 1L, 1L, 1L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 2L, 3L,
                                                      1L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 3L, 2L, 2L, 3L, 2L, 3L,
                                                      1L, 1L, 3L, 1L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L,
                                                      3L, 1L, 3L, 2L, 1L, 1L, 3L, 2L, 2L, 2L, 1L, 1L, 1L, 3L, 1L,
                                                      1L, 1L, 3L, 3L, 3L, 1L, 3L, 3L, 3L, 1L, 2L, 3L, 1L, 3L, 3L,
                                                      3L, 3L, 2L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 1L,
                                                      2L, 2L, 3L, 3L, 1L, 3L, 3L, 1L, 3L, 3L, 1L, 2L, 1L, 2L, 1L,
                                                      1L, 2L, 2L, 1L, 3L, 2L, 2L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 3L,
                                                      2L, 1L, 1L, 1L, 1L, 3L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
                                                      1L, 1L, 2L, 1L, 1L, 2L, 1L, 3L, 2L, 1L, 1L, 3L, 1L, 1L, 1L,
                                                      2L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 2L, 1L, 3L, 1L, 3L, 3L, 2L,
                                                      2L, 3L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 3L, 2L, 3L,
                                                      1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 2L, 2L, 3L,
                                                      3L, 1L, 1L, 1L, 3L, 3L, 3L, 2L, 2L, 3L, 1L, 1L, 1L, 1L, 3L,
                                                      1L, 2L, 1L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 2L, 1L, 1L,
                                                      1L, 1L, 1L, 1L, 3L, 1L, 3L, 2L, 3L, 3L, 3L, 3L, 1L, 1L, 2L,
                                                      1L, 3L, 1L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 3L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 3L, 2L, 1L, 3L, 3L,
                                                      3L, 3L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 2L, 1L, 3L, 3L, 1L, 3L,
                                                      1L, 2L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 2L, 3L, 3L, 3L, 2L, 1L,
                                                      2L, 1L, 3L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 1L,
                                                      1L, 2L, 3L, 2L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                                      2L, 2L, 3L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 3L,
                                                      1L, 2L, 2L, 3L, 1L, 3L, 1L, 3L, 3L, 1L, 3L, 1L, 1L, 2L, 1L,
                                                      1L, 3L, 1L, 1L, 3L, 3L, 2L, 2L, 3L, 1L, 3L, 2L, 1L, 1L, 1L,
                                                      2L, 1L, 2L, 1L, 2L, 3L, 3L, 1L, 2L, 1L, 2L, 1L, 3L, 3L, 1L,
                                                      1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 3L, 3L, 1L,
                                                      1L, 1L, 1L, 2L, 3L, 3L, 1L, 1L, 3L, 2L, 3L, 1L, 3L, 1L, 1L,
                                                      3L, 3L, 1L, 1L, 2L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                                      1L, 2L, 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 2L, 2L, 2L, 1L, 3L,
                                                      1L, 2L, 1L, 3L, 1L, 3L, 3L, 1L, 2L, 1L, 3L, 3L, 3L, 2L, 1L,
                                                      1L, 1L, 1L, 3L, 1L, 3L, 2L, 3L, 3L, 3L, 1L, 3L, 1L, 1L, 3L,
                                                      1L, 1L, 1L, 2L, 1L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 2L,
                                                      1L, 3L, 1L, 2L, 1L, 2L, 3L, 3L, 1L, 2L, 1L, 1L, 3L, 2L, 2L,
                                                      2L, 2L, 1L, 3L, 1L, 3L, 3L, 2L, 1L, 1L, 1L, 2L, 3L, 3L, 1L,
                                                      3L, 3L, 1L, 3L, 2L, 1L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 1L, 3L,
                                                      3L, 2L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 2L, 1L, 3L,
                                                      1L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 1L,
                                                      1L, 3L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 3L, 1L, 3L, 2L, 1L, 1L,
                                                      2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L,
                                                      1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 3L, 1L, 3L, 1L,
                                                      1L, 1L, 1L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 3L, 2L, 3L, 1L, 3L,
                                                      1L, 1L, 2L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 1L, 1L, 1L, 1L,
                                                      3L, 2L, 1L, 3L, 3L, 1L, 1L, 3L, 3L, 3L, 3L, 2L, 1L, 1L, 1L,
                                                      1L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 3L, 1L,
                                                      1L, 1L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 1L, 1L,
                                                      3L, 3L, 1L, 1L, 3L, 2L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 3L, 1L,
                                                      3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 3L,
                                                      2L, 2L, 2L, 1L, 2L, 3L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 1L,
                                                      2L, 1L, 3L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                                      1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 3L, 3L,
                                                      3L, 3L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 3L,
                                                      2L, 3L, 1L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 1L,
                                                      3L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 1L,
                                                      3L, 3L, 3L, 1L, 2L, 1L, 3L, 3L, 1L, 2L, 3L, 1L, 1L, 2L, 1L,
                                                      2L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 1L,
                                                      1L, 1L, 1L, 1L, 3L, 3L, 2L, 1L, 1L, 3L, 3L, 2L, 1L, 3L, 1L,
                                                      2L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 1L, 1L, 2L, 3L, 2L, 1L, 1L,
                                                      3L, 1L, 3L, 3L, 2L, 1L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 2L,
                                                      2L, 1L, 3L, 2L, 1L, 3L, 2L, 1L, 3L, 3L, 1L, 3L, 1L, 2L, 2L,
                                                      1L, 1L, 3L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L,
                                                      1L, 1L, 3L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 1L, 3L, 3L, 1L, 1L,
                                                      1L, 3L, 1L, 2L, 3L, 1L, 2L, 2L, 3L, 2L, 3L, 2L, 1L, 1L, 2L,
                                                      2L, 1L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 2L, 2L, 1L, 2L, 1L, 1L,
                                                      1L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 3L, 2L,
                                                      3L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 1L, 3L, 2L, 1L,
                                                      1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 3L,
                                                      2L, 1L, 1L, 2L, 3L, 1L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, 1L,
                                                      2L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 2L, 2L, 3L, 2L, 1L, 1L,
                                                      2L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 2L, 3L, 3L, 2L, 1L, 3L,
                                                      2L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 2L,
                                                      1L, 1L, 1L, 2L, 1L, 1L, 2L, 3L, 1L, 3L, 1L, 3L, 1L, 2L, 1L,
                                                      3L, 3L, 1L, 1L, 2L, 2L, 1L, 1L, 3L, 2L, 2L, 3L, 2L, 3L, 2L,
                                                      2L, 3L, 2L, 1L, 3L, 1L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 1L,
                                                      2L, 2L, 2L, 2L, 3L, 2L, 2L, 2L, 1L, 1L, 3L, 3L, 1L, 3L, 3L,
                                                      1L, 1L, 1L, 3L, 3L, 2L, 1L, 3L, 1L, 1L, 3L, 3L, 2L, 3L, 2L,
                                                      1L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 1L, 3L,
                                                      3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 2L, 2L, 1L, 1L, 1L,
                                                      1L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 3L, 3L, 2L, 1L, 2L, 1L, 1L,
                                                      1L, 1L, 2L, 3L, 2L, 1L, 1L, 1L, 3L, 2L, 2L, 1L, 3L, 1L, 3L,
                                                      1L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 3L, 1L, 3L, 1L, 3L,
                                                      1L, 1L, 2L, 3L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L,
                                                      3L, 1L, 3L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 3L, 2L, 2L, 1L, 2L,
                                                      2L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 3L,
                                                      1L, 1L, 3L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 3L, 3L, 2L,
                                                      3L, 2L, 2L, 3L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 2L, 3L, 3L,
                                                      1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 3L, 1L,
                                                      3L, 2L, 3L, 1L, 1L, 1L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 1L,
                                                      1L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 1L, 1L, 2L, 1L,
                                                      1L, 2L, 3L, 2L, 3L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
                                                      3L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 3L, 2L, 1L, 1L, 3L, 3L, 3L,
                                                      1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 1L, 3L,
                                                      2L, 2L, 2L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 1L, 1L, 2L, 1L,
                                                      3L, 3L, 3L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 3L,
                                                      2L, 3L, 2L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 2L,
                                                      1L, 3L, 1L, 1L, 1L, 3L, 2L, 2L, 1L, 1L, 3L, 3L, 3L, 1L, 3L,
                                                      3L, 1L, 2L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 2L, 2L,
                                                      1L, 3L, 3L, 2L, 1L, 3L, 3L, 2L, 2L, 3L, 3L, 2L, 1L, 1L, 1L,
                                                      1L, 1L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 1L,
                                                      1L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 3L, 2L, 3L, 3L, 2L, 2L,
                                                      3L, 1L, 2L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 2L, 1L, 2L,
                                                      3L, 2L, 2L, 2L, 3L, 3L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 2L,
                                                      1L, 1L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 3L, 1L, 1L, 3L,
                                                      3L, 2L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 2L,
                                                      3L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
                                                      3L, 3L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 3L, 2L, 1L, 3L, 1L, 2L,
                                                      1L, 1L, 2L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 1L,
                                                      3L, 1L, 1L, 1L, 3L, 2L, 3L, 1L, 3L, 3L, 1L, 1L, 2L, 1L, 1L,
                                                      2L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 1L, 1L, 3L,
                                                      2L, 2L, 1L, 1L, 1L, 2L, 2L, 3L, 1L, 3L, 2L, 1L, 1L, 3L, 1L,
                                                      3L, 1L, 2L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 3L,
                                                      3L, 2L, 1L, 2L, 3L, 1L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 1L, 1L,
                                                      2L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 3L, 3L, 1L, 1L, 1L,
                                                      1L, 3L, 2L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
                                                      1L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 2L, 1L, 1L, 3L, 2L, 1L,
                                                      1L, 3L, 1L, 3L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 3L, 1L, 1L,
                                                      2L, 3L, 3L, 2L, 1L, 3L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 3L, 1L,
                                                      1L, 1L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 3L,
                                                      1L, 3L, 1L, 2L, 3L, 3L, 3L, 1L, 3L, 1L, 3L, 3L, 2L, 1L, 3L,
                                                      1L, 2L, 1L, 3L, 2L, 2L, 3L, 2L, 1L, 1L, 3L, 2L, 1L, 3L, 1L,
                                                      3L, 1L, 2L, 1L, 3L, 3L, 3L, 1L, 2L, 2L, 3L, 3L, 1L, 3L, 1L,
                                                      1L, 3L, 3L, 1L, 1L, 1L, 1L, 3L, 3L, 2L, 1L, 1L, 1L, 2L, 1L,
                                                      2L, 3L, 1L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L,
                                                      1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 3L,
                                                      1L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 3L, 1L, 1L, 3L, 1L,
                                                      1L, 1L, 1L, 1L, 1L, 2L, 3L, 3L, 1L, 2L, 1L, 1L, 2L, 1L, 3L,
                                                      1L, 2L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 3L, 2L, 1L, 3L, 1L, 3L,
                                                      3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L,
                                                      1L, 1L, 1L, 2L, 3L, 3L, 3L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 3L,
                                                      2L, 1L, 3L, 3L, 1L, 1L, 3L, 2L, 2L, 2L, 2L, 3L, 2L, 2L, 1L,
                                                      1L, 1L, 1L, 2L, 3L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 1L, 1L,
                                                      1L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 2L, 1L, 1L, 3L, 3L, 2L, 1L,
                                                      2L, 1L, 1L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 2L,
                                                      3L, 3L, 2L, 1L, 3L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 2L, 2L, 2L,
                                                      3L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L,
                                                      1L, 1L, 1L, 3L, 1L, 1L, 2L, 1L, 2L, 1L, 3L, 1L, 2L, 3L, 1L,
                                                      1L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 3L, 3L,
                                                      1L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 3L,
                                                      1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 2L, 3L, 2L,
                                                      1L, 1L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, 3L, 2L, 1L, 2L, 1L, 3L,
                                                      1L, 3L, 2L, 3L, 1L, 1L, 3L, 1L, 3L, 3L, 2L, 3L, 3L, 3L, 1L,
                                                      1L, 3L, 2L, 3L, 3L, 2L, 1L, 1L, 1L, 2L, 2L, 3L, 3L, 2L, 1L,
                                                      2L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 3L, 1L, 1L, 1L, 3L, 2L, 3L,
                                                      3L, 1L, 2L, 2L, 2L, 1L, 2L, 3L, 2L, 3L, 3L, 1L, 1L, 3L, 3L,
                                                      1L, 3L, 3L, 3L, 1L, 2L, 2L, 3L, 1L, 1L, 1L, 3L, 3L, 1L, 3L,
                                                      1L, 2L, 3L, 3L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 3L, 2L, 2L, 2L,
                                                      1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 1L,
                                                      1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 3L, 2L, 1L, 1L, 3L, 1L,
                                                      1L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 2L,
                                                      3L, 1L, 1L, 1L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                                      3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L,
                                                      2L, 1L, 1L, 3L, 3L, 2L, 1L, 1L, 1L, 1L, 2L, 3L, 3L, 1L, 2L,
                                                      1L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 1L,
                                                      1L, 1L, 1L, 3L, 3L, 3L, 2L, 3L, 2L, 1L, 1L, 1L, 3L, 1L, 3L,
                                                      2L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 3L,
                                                      3L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 3L, 1L, 1L,
                                                      1L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 2L, 3L,
                                                      1L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 1L,
                                                      3L, 3L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 1L,
                                                      1L, 1L, 1L, 1L, 2L, 3L, 1L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L,
                                                      1L, 3L), class = "factor", .Label = c("No", "No internet service",
                                                                                            "Yes"), questiontype = "PickOne", name = "OnlineSecurity_cat", label = "OnlineSecurity", question = "OnlineSecurity"),
                     OnlineBackup_cat = structure(c(3L, 1L, 3L, 1L, 1L, 1L, 3L,
                                                    1L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 3L, 2L, 1L, 1L, 3L, 1L, 2L,
                                                    2L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 1L,
                                                    1L, 3L, 1L, 3L, 3L, 2L, 3L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 3L,
                                                    1L, 3L, 3L, 1L, 1L, 3L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 3L, 3L,
                                                    3L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 3L, 1L, 3L, 3L, 2L, 1L, 1L,
                                                    1L, 3L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, 1L, 3L, 3L, 1L, 3L,
                                                    2L, 2L, 3L, 2L, 2L, 1L, 3L, 3L, 1L, 3L, 1L, 1L, 2L, 3L, 1L,
                                                    3L, 1L, 3L, 3L, 1L, 1L, 2L, 3L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
                                                    2L, 2L, 3L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 3L, 1L,
                                                    3L, 3L, 2L, 3L, 2L, 1L, 3L, 3L, 1L, 1L, 3L, 3L, 2L, 1L, 1L,
                                                    2L, 1L, 2L, 3L, 1L, 1L, 3L, 2L, 2L, 1L, 3L, 3L, 2L, 1L, 1L,
                                                    3L, 1L, 2L, 2L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 1L, 3L, 1L, 3L,
                                                    1L, 2L, 3L, 1L, 3L, 2L, 3L, 2L, 3L, 2L, 3L, 3L, 2L, 1L, 3L,
                                                    1L, 1L, 1L, 3L, 3L, 1L, 1L, 3L, 1L, 1L, 2L, 2L, 1L, 3L, 3L,
                                                    3L, 3L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 3L, 3L, 3L,
                                                    1L, 2L, 2L, 3L, 1L, 1L, 3L, 2L, 3L, 3L, 1L, 3L, 3L, 1L, 1L,
                                                    3L, 1L, 3L, 3L, 1L, 3L, 3L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 3L,
                                                    3L, 3L, 3L, 3L, 2L, 3L, 2L, 2L, 1L, 3L, 1L, 3L, 1L, 3L, 3L,
                                                    3L, 1L, 3L, 3L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 3L,
                                                    3L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 2L, 1L,
                                                    1L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, 3L,
                                                    1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 2L, 2L, 3L, 1L, 1L, 3L, 3L,
                                                    3L, 3L, 3L, 3L, 3L, 3L, 2L, 2L, 1L, 1L, 2L, 1L, 3L, 1L, 1L,
                                                    1L, 3L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 2L, 1L, 1L, 1L,
                                                    2L, 1L, 3L, 2L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 3L,
                                                    3L, 3L, 3L, 2L, 3L, 3L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 1L,
                                                    3L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 3L, 2L, 2L, 3L, 2L,
                                                    1L, 3L, 1L, 3L, 3L, 2L, 3L, 1L, 2L, 1L, 3L, 2L, 3L, 1L, 3L,
                                                    1L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 1L, 1L, 1L,
                                                    3L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 1L, 2L, 3L, 3L,
                                                    3L, 2L, 1L, 2L, 3L, 1L, 3L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 1L,
                                                    1L, 1L, 3L, 3L, 3L, 3L, 1L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 3L,
                                                    3L, 1L, 1L, 3L, 3L, 1L, 3L, 2L, 3L, 3L, 2L, 3L, 3L, 3L, 1L,
                                                    1L, 1L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 3L, 3L, 1L, 1L,
                                                    1L, 1L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 2L, 3L, 2L, 2L,
                                                    1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 3L, 1L, 2L, 1L, 1L, 1L, 3L,
                                                    3L, 3L, 2L, 3L, 3L, 2L, 2L, 3L, 1L, 2L, 3L, 1L, 1L, 3L, 2L,
                                                    1L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 3L, 3L, 3L, 1L,
                                                    1L, 3L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 3L, 2L, 3L, 3L, 1L, 2L,
                                                    3L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 1L,
                                                    1L, 3L, 1L, 3L, 3L, 2L, 3L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 3L,
                                                    1L, 2L, 2L, 1L, 3L, 3L, 3L, 3L, 3L, 1L, 3L, 2L, 1L, 3L, 1L,
                                                    3L, 1L, 1L, 2L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 1L,
                                                    2L, 2L, 2L, 1L, 3L, 3L, 2L, 2L, 1L, 1L, 2L, 3L, 2L, 1L, 1L,
                                                    1L, 1L, 3L, 2L, 2L, 1L, 2L, 3L, 1L, 2L, 1L, 3L, 3L, 1L, 1L,
                                                    1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 3L, 2L, 1L, 2L, 2L, 3L,
                                                    1L, 3L, 1L, 1L, 1L, 1L, 2L, 3L, 3L, 3L, 3L, 1L, 3L, 2L, 1L,
                                                    2L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L,
                                                    1L, 3L, 3L, 1L, 2L, 3L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 1L, 1L,
                                                    1L, 2L, 1L, 3L, 3L, 1L, 2L, 1L, 3L, 3L, 1L, 2L, 3L, 1L, 2L,
                                                    2L, 3L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 1L,
                                                    2L, 1L, 1L, 3L, 3L, 3L, 3L, 1L, 3L, 1L, 3L, 1L, 3L, 3L, 1L,
                                                    1L, 3L, 3L, 1L, 3L, 2L, 1L, 1L, 3L, 1L, 2L, 2L, 1L, 1L, 1L,
                                                    2L, 3L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 1L, 1L,
                                                    3L, 3L, 3L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 3L, 2L,
                                                    3L, 3L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 3L,
                                                    1L, 3L, 3L, 3L, 3L, 2L, 1L, 2L, 1L, 3L, 3L, 3L, 3L, 2L, 1L,
                                                    3L, 3L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 3L, 2L, 3L, 1L, 1L, 1L,
                                                    1L, 1L, 3L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 3L, 1L, 3L,
                                                    1L, 1L, 1L, 3L, 3L, 3L, 1L, 3L, 2L, 1L, 1L, 3L, 3L, 1L, 1L,
                                                    3L, 2L, 3L, 3L, 3L, 1L, 2L, 2L, 1L, 1L, 3L, 1L, 3L, 2L, 2L,
                                                    1L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 3L, 3L, 2L, 1L, 1L, 1L, 3L,
                                                    1L, 3L, 2L, 2L, 3L, 1L, 3L, 3L, 1L, 2L, 1L, 1L, 2L, 1L, 3L,
                                                    1L, 1L, 1L, 1L, 2L, 1L, 3L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
                                                    2L, 3L, 1L, 1L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 1L, 2L, 2L,
                                                    1L, 1L, 2L, 3L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 3L, 1L,
                                                    1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 3L,
                                                    1L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 1L, 1L, 3L, 1L, 1L, 3L, 1L,
                                                    1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 1L, 3L, 1L, 2L,
                                                    1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                                    1L, 1L, 1L, 2L, 3L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 3L,
                                                    1L, 1L, 2L, 3L, 2L, 3L, 3L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L,
                                                    1L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 2L, 2L,
                                                    3L, 3L, 2L, 1L, 3L, 2L, 2L, 3L, 3L, 1L, 3L, 1L, 3L, 1L, 2L,
                                                    1L, 3L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 1L, 3L, 2L, 1L, 2L, 1L,
                                                    1L, 2L, 3L, 3L, 2L, 2L, 1L, 2L, 3L, 2L, 1L, 3L, 1L, 1L, 1L,
                                                    1L, 1L, 1L, 3L, 2L, 1L, 1L, 2L, 3L, 2L, 3L, 3L, 1L, 1L, 3L,
                                                    1L, 3L, 3L, 2L, 1L, 1L, 2L, 3L, 3L, 3L, 3L, 2L, 3L, 1L, 3L,
                                                    1L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L,
                                                    1L, 1L, 3L, 3L, 3L, 2L, 2L, 1L, 3L, 3L, 3L, 2L, 1L, 1L, 1L,
                                                    1L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 3L, 1L, 1L, 1L,
                                                    1L, 1L, 1L, 1L, 2L, 3L, 1L, 1L, 3L, 1L, 1L, 2L, 3L, 3L, 1L,
                                                    2L, 1L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 3L, 3L, 1L, 1L, 1L, 3L,
                                                    2L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 1L,
                                                    3L, 3L, 3L, 2L, 3L, 2L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 3L, 2L,
                                                    1L, 1L, 2L, 1L, 1L, 3L, 2L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 1L,
                                                    1L, 3L, 1L, 3L, 3L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 3L,
                                                    1L, 3L, 3L, 2L, 2L, 2L, 1L, 2L, 3L, 3L, 2L, 2L, 2L, 1L, 3L,
                                                    1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 3L, 2L, 2L, 3L, 3L, 1L,
                                                    2L, 1L, 2L, 1L, 1L, 2L, 1L, 3L, 3L, 2L, 1L, 2L, 1L, 2L, 1L,
                                                    3L, 1L, 1L, 1L, 3L, 1L, 3L, 3L, 3L, 1L, 3L, 1L, 3L, 2L, 1L,
                                                    3L, 2L, 3L, 2L, 1L, 3L, 3L, 3L, 3L, 1L, 2L, 1L, 1L, 1L, 3L,
                                                    2L, 1L, 3L, 3L, 3L, 2L, 2L, 3L, 1L, 1L, 1L, 1L, 2L, 2L, 3L,
                                                    1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 1L,
                                                    3L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 2L, 1L,
                                                    2L, 3L, 1L, 3L, 1L, 1L, 1L, 1L, 2L, 3L, 1L, 1L, 3L, 1L, 1L,
                                                    1L, 2L, 2L, 2L, 1L, 1L, 3L, 2L, 3L, 3L, 1L, 2L, 3L, 3L, 1L,
                                                    2L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 3L, 2L,
                                                    3L, 3L, 1L, 1L, 3L, 1L, 3L, 3L, 1L, 3L, 3L, 1L, 3L, 3L, 2L,
                                                    3L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
                                                    2L, 3L, 1L, 3L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 3L, 2L, 3L,
                                                    3L, 1L, 3L, 2L, 3L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 3L, 3L,
                                                    3L, 3L, 1L, 3L, 2L, 2L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 1L, 2L,
                                                    3L, 1L, 2L, 3L, 3L, 3L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 3L,
                                                    1L, 3L, 1L, 2L, 2L, 1L, 3L, 2L, 3L, 3L, 1L, 1L, 1L, 3L, 3L,
                                                    1L, 1L, 3L, 1L, 1L, 2L, 3L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 1L,
                                                    3L, 2L, 3L, 1L, 3L, 1L, 1L, 3L, 2L, 1L, 3L, 2L, 1L, 3L, 3L,
                                                    3L, 2L, 3L, 2L, 2L, 1L, 3L, 3L, 1L, 1L, 3L, 3L, 3L, 1L, 1L,
                                                    3L, 3L, 3L, 3L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 2L, 3L,
                                                    2L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 2L, 1L, 3L,
                                                    2L, 1L, 3L, 2L, 3L, 1L, 1L, 1L, 1L, 2L, 2L, 3L, 1L, 1L, 3L,
                                                    3L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 1L, 3L,
                                                    2L, 2L, 3L, 3L, 2L, 1L, 3L, 1L, 3L, 1L, 3L, 3L, 2L, 2L, 3L,
                                                    1L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 2L, 3L, 3L, 3L, 2L, 1L,
                                                    2L, 2L, 3L, 3L, 1L, 3L, 2L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 1L,
                                                    3L, 2L, 1L, 3L, 2L, 1L, 3L, 1L, 2L, 3L, 3L, 2L, 3L, 2L, 3L,
                                                    1L, 2L, 3L, 1L, 1L, 1L, 3L, 3L, 3L, 1L, 3L, 2L, 2L, 1L, 2L,
                                                    3L, 1L, 1L, 3L, 2L, 3L, 1L, 3L, 3L, 1L, 1L, 2L, 1L, 1L, 2L,
                                                    1L, 2L, 3L, 2L, 3L, 1L, 1L, 2L, 3L, 3L, 1L, 2L, 3L, 1L, 3L,
                                                    3L, 2L, 3L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 3L, 2L, 3L, 2L,
                                                    1L, 3L, 1L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 1L, 3L, 1L, 1L,
                                                    1L, 3L, 2L, 3L, 3L, 1L, 2L, 1L, 2L, 3L, 1L, 1L, 1L, 1L, 1L,
                                                    2L, 3L, 2L, 1L, 2L, 1L, 2L, 3L, 3L, 2L, 2L, 2L, 1L, 3L, 1L,
                                                    1L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, 2L, 1L, 3L, 2L, 1L, 3L, 1L,
                                                    3L, 1L, 2L, 1L, 3L, 2L, 3L, 3L, 3L, 1L, 3L, 2L, 1L, 1L, 3L,
                                                    1L, 3L, 3L, 3L, 1L, 1L, 3L, 3L, 2L, 1L, 3L, 3L, 1L, 3L, 3L,
                                                    3L, 1L, 3L, 2L, 2L, 3L, 1L, 3L, 2L, 3L, 3L, 2L, 2L, 3L, 3L,
                                                    2L, 3L, 1L, 1L, 3L, 3L, 1L, 1L, 2L, 3L, 1L, 2L, 1L, 1L, 1L,
                                                    1L, 2L, 1L, 2L, 3L, 2L, 2L, 3L, 2L, 3L, 2L, 2L, 2L, 3L, 1L,
                                                    2L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 3L,
                                                    1L, 3L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 2L,
                                                    1L, 1L, 1L, 2L, 1L, 3L, 3L, 2L, 3L, 1L, 2L, 1L, 3L, 3L, 3L,
                                                    3L, 3L, 1L, 1L, 3L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                                    1L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 1L, 1L,
                                                    2L, 1L, 3L, 3L, 3L, 3L, 3L, 1L, 3L, 3L, 2L, 2L, 3L, 3L, 1L,
                                                    1L, 2L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 3L, 1L, 2L, 3L, 1L,
                                                    1L, 1L, 3L, 3L, 2L, 1L, 3L, 1L, 1L, 3L, 1L, 3L, 3L, 3L, 1L,
                                                    2L, 1L, 2L, 1L, 2L, 3L, 3L, 1L, 3L, 3L, 2L, 2L, 3L, 1L, 1L,
                                                    1L, 3L, 3L, 3L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 2L,
                                                    3L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                                    3L, 1L, 2L, 2L, 2L, 1L, 3L, 3L, 3L, 1L, 3L, 1L, 2L, 2L, 2L,
                                                    1L, 3L, 1L, 1L, 1L, 3L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 3L, 3L,
                                                    2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 3L, 2L, 2L, 1L, 1L, 2L,
                                                    1L, 1L, 2L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 3L, 1L, 3L, 2L, 3L,
                                                    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 3L, 2L, 2L, 3L, 3L,
                                                    1L, 1L, 1L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 3L, 2L, 1L, 2L, 2L,
                                                    1L, 1L, 2L, 3L, 3L, 1L, 3L, 3L, 3L, 3L, 1L, 1L, 2L, 1L, 1L,
                                                    2L, 2L, 3L, 1L, 1L, 3L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 3L, 1L,
                                                    2L, 3L, 1L, 2L, 1L, 2L, 3L, 3L, 3L, 1L, 3L, 1L, 1L, 3L, 2L,
                                                    2L, 3L, 3L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 3L, 3L, 1L, 3L,
                                                    1L, 1L, 2L, 1L, 1L, 1L, 3L, 3L, 3L, 1L, 3L, 2L, 1L, 1L, 1L,
                                                    1L, 2L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
                                                    3L, 3L, 1L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 3L, 1L,
                                                    3L, 1L, 3L, 3L, 1L, 3L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 2L,
                                                    2L, 3L, 1L, 3L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 3L, 3L, 2L,
                                                    1L, 3L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 3L,
                                                    2L, 1L, 3L, 1L, 3L, 2L, 1L, 2L, 3L, 1L, 3L, 2L, 3L, 2L, 1L,
                                                    1L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 3L, 3L,
                                                    3L, 1L, 3L, 3L, 2L, 3L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 2L, 1L,
                                                    1L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 3L, 1L, 3L,
                                                    1L, 2L, 3L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 1L,
                                                    1L, 2L, 3L, 2L, 3L, 1L, 1L, 3L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
                                                    3L, 1L, 2L, 2L, 1L, 1L, 3L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 3L,
                                                    1L, 1L, 2L, 3L, 2L, 3L, 1L, 2L, 2L, 2L, 3L, 1L, 1L, 1L, 2L,
                                                    1L, 3L, 2L, 2L, 3L, 3L, 2L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 2L,
                                                    1L, 3L, 2L, 1L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 2L, 2L,
                                                    2L, 3L, 3L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 3L, 2L, 1L, 1L,
                                                    1L, 2L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 2L, 2L, 3L, 2L,
                                                    1L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 3L, 2L, 3L, 1L, 2L, 3L, 1L,
                                                    1L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
                                                    1L, 2L, 3L, 3L, 3L, 1L, 3L, 1L, 2L, 3L, 3L, 2L, 2L, 1L, 1L,
                                                    2L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 3L, 2L, 2L,
                                                    2L, 1L, 1L, 3L, 3L, 2L, 2L, 3L, 1L, 3L, 3L, 1L, 3L, 1L, 3L,
                                                    3L, 3L, 1L, 2L, 3L, 1L, 1L, 3L, 1L, 1L, 3L, 3L, 1L, 3L, 1L,
                                                    2L, 2L, 3L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 2L, 3L, 1L, 1L, 1L,
                                                    3L, 3L, 1L, 2L, 3L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 3L, 2L, 3L,
                                                    2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 1L, 1L, 3L,
                                                    1L, 3L, 3L, 3L, 3L, 3L, 2L, 3L, 1L, 3L, 2L, 1L, 2L, 2L, 2L,
                                                    1L, 2L, 1L, 3L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 3L, 3L, 1L, 1L,
                                                    1L, 2L, 2L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
                                                    1L, 1L, 3L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 3L, 3L, 1L, 1L, 1L,
                                                    2L, 2L, 2L, 1L, 2L, 1L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 1L, 3L,
                                                    1L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L,
                                                    1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 3L, 3L, 1L, 3L,
                                                    1L, 2L, 2L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 2L, 3L, 1L, 3L, 3L,
                                                    1L, 3L, 1L, 3L, 3L, 2L, 3L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 1L,
                                                    1L, 1L, 2L, 2L, 3L, 1L, 2L, 1L, 3L, 3L, 2L, 1L, 3L, 1L, 2L,
                                                    3L, 2L, 3L, 1L, 3L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 2L, 2L, 1L,
                                                    3L, 2L, 1L, 3L, 3L, 3L, 3L, 2L, 3L, 3L, 2L, 2L, 2L, 3L, 1L,
                                                    1L, 2L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 1L, 1L, 2L, 1L,
                                                    3L, 2L, 3L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 2L, 3L, 1L, 1L, 1L,
                                                    2L, 1L, 2L, 1L, 2L, 3L, 1L, 3L, 1L, 1L, 1L, 2L, 3L, 3L, 1L,
                                                    1L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 2L, 2L, 2L, 3L, 3L, 1L, 3L,
                                                    1L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 3L, 3L, 1L, 3L, 1L,
                                                    2L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 3L, 2L, 3L,
                                                    3L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 2L, 2L, 3L, 1L, 1L,
                                                    3L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 1L, 3L, 3L, 2L, 3L, 1L, 3L,
                                                    1L, 2L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 3L, 3L, 3L, 3L, 1L, 2L,
                                                    2L, 3L, 1L, 2L, 2L, 2L, 3L, 2L, 3L, 1L, 2L, 3L, 2L, 1L, 1L,
                                                    3L, 2L, 3L, 1L, 1L, 3L, 3L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
                                                    3L, 2L, 2L, 1L, 2L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 2L,
                                                    2L, 3L, 2L, 2L, 1L, 2L, 3L, 1L, 1L, 1L, 2L, 3L, 1L, 1L, 1L,
                                                    2L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 3L,
                                                    1L, 1L, 3L, 1L, 1L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L,
                                                    3L, 3L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 1L,
                                                    1L, 2L, 2L, 3L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 1L, 3L,
                                                    2L, 3L, 2L, 3L, 1L, 1L, 2L, 1L, 1L, 2L, 3L, 3L, 2L, 2L, 3L,
                                                    3L, 1L, 1L, 3L, 3L, 3L, 2L, 1L, 2L, 1L, 2L, 1L, 3L, 2L, 3L,
                                                    3L, 2L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 1L, 3L, 1L, 1L, 1L, 3L,
                                                    2L, 3L, 2L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 2L,
                                                    1L, 1L, 1L, 3L, 2L, 1L, 3L, 3L, 2L, 1L, 3L, 2L, 3L, 3L, 2L,
                                                    3L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 3L, 1L, 1L, 3L, 1L, 2L,
                                                    3L, 1L, 2L, 1L, 3L, 2L, 2L, 3L, 3L, 2L, 3L, 3L, 2L, 3L, 3L,
                                                    1L, 3L, 2L, 3L, 2L, 2L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 1L,
                                                    2L, 3L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 3L,
                                                    3L, 1L, 2L, 3L, 3L, 2L, 2L, 1L, 3L, 2L, 2L, 3L, 1L, 3L, 1L,
                                                    3L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, 3L, 3L, 3L, 1L, 1L, 3L, 3L,
                                                    1L, 3L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 1L,
                                                    2L, 3L, 1L, 3L, 3L, 3L, 2L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 1L,
                                                    3L, 3L, 1L, 3L, 1L, 1L, 2L, 3L, 2L, 1L, 3L, 3L, 3L, 1L, 3L,
                                                    3L, 2L, 2L, 1L, 3L, 2L, 2L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 2L,
                                                    1L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 2L, 3L, 2L, 2L,
                                                    1L, 1L, 3L, 1L, 1L, 3L, 2L, 1L, 3L, 1L, 2L, 3L, 1L, 1L, 3L,
                                                    1L, 3L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 3L, 3L, 3L, 1L, 2L, 1L,
                                                    3L, 3L, 1L, 3L, 2L, 3L, 1L, 3L, 2L, 2L, 2L, 3L, 2L, 1L, 1L,
                                                    2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 3L, 3L, 3L,
                                                    3L, 3L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 2L, 2L, 3L, 3L, 1L, 3L,
                                                    3L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L,
                                                    1L, 1L, 2L, 3L, 1L, 3L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 3L,
                                                    1L, 3L, 1L, 3L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 3L, 1L, 1L,
                                                    2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
                                                    3L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 1L, 3L,
                                                    2L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 1L,
                                                    1L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 2L, 2L, 1L, 3L, 1L,
                                                    3L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 1L, 2L,
                                                    1L, 2L, 3L, 3L, 3L, 3L, 3L, 1L, 3L, 1L, 3L, 3L, 3L, 1L, 1L,
                                                    3L, 1L, 3L, 1L, 1L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 2L, 1L, 1L,
                                                    3L, 1L, 3L, 3L, 3L, 3L, 3L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L,
                                                    3L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 3L, 1L, 2L, 3L,
                                                    1L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 3L, 2L, 3L, 1L, 2L, 3L, 1L,
                                                    1L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 3L, 1L,
                                                    3L, 1L, 3L, 2L, 3L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 2L, 2L,
                                                    2L, 3L, 1L, 3L, 1L, 3L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
                                                    1L, 3L, 3L, 2L, 3L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 1L,
                                                    1L, 1L, 3L, 2L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 3L, 2L, 1L, 1L,
                                                    1L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 3L, 1L,
                                                    1L, 3L, 3L, 2L, 2L, 1L, 2L, 3L, 1L, 1L, 2L, 2L, 1L, 2L, 3L,
                                                    1L, 1L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 2L, 3L, 2L, 2L, 1L, 1L,
                                                    1L, 3L, 2L, 3L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 2L, 1L, 3L,
                                                    3L, 1L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
                                                    1L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 2L, 1L, 1L, 3L, 2L, 2L, 1L,
                                                    1L, 1L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 1L,
                                                    1L, 3L, 2L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L,
                                                    2L, 3L, 3L, 1L, 3L, 3L, 2L, 2L, 1L, 1L, 2L, 3L, 3L, 1L, 3L,
                                                    2L, 3L, 1L, 3L, 1L, 3L, 3L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 1L,
                                                    3L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 2L, 3L, 1L, 1L, 1L, 1L, 1L,
                                                    2L, 3L, 3L, 3L, 2L, 2L, 1L, 3L, 3L, 3L, 2L, 3L, 3L, 1L, 3L,
                                                    2L, 3L, 3L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 3L,
                                                    1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 2L, 3L, 1L,
                                                    2L, 3L, 3L, 2L, 2L, 3L, 2L, 3L, 2L, 3L, 1L, 3L, 2L, 1L, 1L,
                                                    1L, 3L, 2L, 3L, 1L, 3L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 3L,
                                                    1L, 1L, 1L, 3L, 3L, 2L, 1L, 1L, 1L, 3L, 1L, 2L, 3L, 2L, 1L,
                                                    2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 3L,
                                                    3L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 3L,
                                                    2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 3L, 1L,
                                                    2L, 1L, 2L, 3L, 3L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 3L, 1L, 2L,
                                                    3L, 3L, 1L, 1L, 3L, 3L, 2L, 3L, 2L, 2L, 2L, 1L, 3L, 2L, 2L,
                                                    3L, 1L, 3L, 1L, 1L, 1L, 3L, 3L, 3L, 2L, 2L, 2L, 1L, 1L, 3L,
                                                    1L, 3L, 3L, 1L, 3L, 3L, 3L, 1L, 3L, 2L, 2L, 2L, 1L, 1L, 1L,
                                                    3L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 3L, 3L,
                                                    2L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 3L, 3L, 2L, 1L, 1L, 1L,
                                                    1L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 1L, 3L,
                                                    2L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 2L, 1L,
                                                    1L, 1L, 3L, 1L, 1L, 3L, 2L, 1L, 3L, 3L, 3L, 2L, 2L, 1L, 2L,
                                                    1L, 3L, 2L, 1L, 3L, 3L, 1L, 1L, 3L, 2L, 2L, 3L, 1L, 3L, 2L,
                                                    1L, 3L, 3L, 3L, 2L, 2L, 1L, 3L, 3L, 1L, 3L, 1L, 1L, 3L, 1L,
                                                    2L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 2L, 3L, 1L, 1L,
                                                    3L, 3L, 3L, 1L, 2L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 1L, 2L, 2L,
                                                    1L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 2L, 1L, 3L, 1L, 3L,
                                                    2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 3L, 1L, 3L,
                                                    1L, 3L, 3L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 1L, 2L, 3L, 2L, 2L,
                                                    3L, 1L, 2L, 2L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 2L, 3L, 2L,
                                                    1L, 2L, 3L, 3L, 3L, 2L, 1L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L,
                                                    1L, 1L, 3L, 1L, 2L, 3L, 1L, 2L, 1L, 3L, 1L, 3L, 3L, 1L, 3L,
                                                    3L, 3L, 3L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 2L, 3L, 2L, 2L, 3L,
                                                    1L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 3L, 1L,
                                                    1L, 1L, 3L, 2L, 2L, 1L, 2L, 2L, 2L, 3L, 1L, 1L, 1L, 3L, 3L,
                                                    3L, 3L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L,
                                                    1L, 1L, 1L, 3L, 2L, 1L, 3L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L,
                                                    1L, 1L, 3L, 2L, 3L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 2L, 1L, 2L,
                                                    2L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
                                                    2L, 2L, 2L, 3L, 3L, 1L, 2L, 1L, 2L, 1L, 1L, 3L, 3L, 2L, 3L,
                                                    2L, 2L, 1L, 3L, 1L, 2L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 3L,
                                                    3L, 3L, 3L, 3L, 3L, 2L, 1L, 3L, 3L, 1L, 2L, 3L, 2L, 3L, 3L,
                                                    1L, 3L, 2L, 1L, 3L, 3L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 3L, 1L,
                                                    3L, 1L, 3L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 1L, 2L, 3L, 1L,
                                                    3L, 3L, 3L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 1L, 3L, 3L, 1L, 1L,
                                                    1L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
                                                    1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 2L,
                                                    2L, 2L, 3L, 1L, 3L, 3L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 2L, 3L,
                                                    1L, 2L, 3L, 3L, 3L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 3L, 2L, 3L,
                                                    2L, 1L, 3L, 3L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 1L, 1L, 1L,
                                                    3L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 3L, 3L, 3L, 3L, 2L, 3L,
                                                    2L, 3L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 3L, 3L, 3L, 2L, 3L, 3L,
                                                    3L, 3L, 1L, 2L, 1L, 3L, 2L, 3L, 2L, 2L, 1L, 1L, 3L, 2L, 2L,
                                                    3L, 3L, 1L, 1L, 3L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 3L, 3L, 1L,
                                                    1L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 2L, 1L, 1L, 1L, 3L, 2L,
                                                    3L, 3L, 2L, 3L, 1L, 2L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L,
                                                    3L, 1L, 2L, 3L, 1L, 2L, 2L, 2L, 2L, 2L, 3L, 1L, 1L, 1L, 1L,
                                                    1L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 2L, 1L, 2L, 1L, 2L, 1L, 1L,
                                                    1L, 1L, 1L, 2L, 3L, 2L, 1L, 1L, 3L, 2L, 2L, 1L, 2L, 3L, 3L,
                                                    1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 3L,
                                                    1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 3L, 3L, 1L, 3L,
                                                    3L, 1L, 3L, 3L, 1L, 3L, 3L, 3L, 3L, 2L, 3L, 1L, 3L, 3L, 3L,
                                                    1L, 2L, 1L, 1L, 2L, 3L, 3L, 3L, 1L, 3L, 2L, 1L, 3L, 1L, 2L,
                                                    2L, 3L, 1L, 3L, 3L, 3L, 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 1L,
                                                    2L, 2L, 1L, 3L, 2L, 2L, 1L, 2L, 1L, 3L, 3L, 2L, 1L, 3L, 2L,
                                                    1L, 3L, 1L, 1L, 3L, 2L, 2L, 2L, 2L, 1L, 3L, 3L, 1L, 3L, 1L,
                                                    3L, 2L, 1L, 1L, 2L, 1L, 3L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L,
                                                    3L, 1L, 2L, 2L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 1L, 3L, 2L, 2L,
                                                    3L, 1L, 2L, 3L, 1L, 3L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 1L, 1L,
                                                    1L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 3L, 3L, 3L, 2L, 2L, 1L, 3L,
                                                    1L, 3L, 1L, 3L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 1L,
                                                    2L, 3L, 3L, 3L, 3L, 1L, 3L, 3L, 3L, 3L, 1L, 2L, 3L, 1L, 1L,
                                                    1L, 1L, 3L, 3L, 3L, 1L, 2L, 3L, 3L, 3L, 3L, 1L, 1L, 2L, 1L,
                                                    3L, 1L, 1L, 3L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 1L,
                                                    1L, 1L, 3L, 1L, 3L, 1L, 3L, 3L, 2L, 3L, 2L, 3L, 3L, 3L, 3L,
                                                    1L, 3L, 3L, 3L, 3L, 2L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 3L,
                                                    2L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 2L, 3L, 3L, 1L, 2L, 1L, 2L,
                                                    1L, 3L, 2L, 2L, 1L, 1L, 1L, 3L, 3L, 1L, 3L, 2L, 1L, 1L, 1L,
                                                    2L, 3L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 2L,
                                                    2L, 3L, 3L, 3L, 3L, 2L, 1L, 2L, 2L, 1L, 3L, 3L, 3L, 1L, 1L,
                                                    2L, 2L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 1L,
                                                    1L, 1L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 3L, 2L, 1L, 3L, 1L, 2L,
                                                    3L, 2L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L,
                                                    3L, 2L, 3L, 1L, 1L, 1L, 2L, 1L, 3L, 2L, 2L, 1L, 3L, 1L, 1L,
                                                    1L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L,
                                                    1L, 3L, 3L, 2L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 1L,
                                                    2L, 1L, 3L, 3L, 3L, 2L, 3L, 2L, 1L, 2L, 2L, 2L, 1L, 3L, 3L,
                                                    2L, 1L, 3L, 1L, 3L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 3L, 1L,
                                                    3L, 1L, 3L, 1L, 1L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 3L,
                                                    3L, 3L, 2L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 2L, 1L,
                                                    3L, 3L, 2L, 1L, 2L, 3L, 3L, 3L, 2L, 1L, 1L, 3L, 2L, 2L, 2L,
                                                    2L, 3L, 1L, 1L, 3L, 3L, 2L, 1L, 3L, 3L, 2L, 3L, 1L, 1L, 1L,
                                                    3L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 3L, 3L,
                                                    2L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 2L, 2L, 3L, 3L, 3L,
                                                    3L, 1L, 3L, 3L, 2L, 3L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 3L, 1L,
                                                    3L, 1L, 3L, 2L, 3L, 2L, 2L, 2L, 1L, 3L, 3L, 2L, 1L, 3L, 2L,
                                                    1L, 1L, 1L, 1L, 1L, 2L, 3L, 1L, 1L, 3L, 3L, 3L, 3L, 3L, 3L,
                                                    1L, 1L, 1L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 1L,
                                                    1L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 1L,
                                                    3L, 2L, 3L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 3L, 1L,
                                                    2L, 1L, 3L, 3L, 3L, 1L, 1L, 3L, 3L, 1L, 2L, 3L, 1L, 1L, 1L,
                                                    3L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 2L, 1L, 1L, 3L, 1L, 3L,
                                                    1L, 3L, 1L, 3L, 3L, 3L, 3L, 1L, 2L, 2L, 2L, 3L, 1L, 3L, 3L,
                                                    3L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 3L,
                                                    3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
                                                    2L, 2L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 2L,
                                                    1L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
                                                    3L, 1L, 3L, 1L, 2L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 3L, 3L, 1L,
                                                    3L, 2L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 3L, 3L, 3L, 1L, 3L, 2L,
                                                    3L, 1L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 1L,
                                                    1L, 3L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 1L, 3L,
                                                    3L, 3L, 1L, 2L, 3L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 3L, 2L,
                                                    3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 1L,
                                                    1L, 1L, 1L, 1L, 1L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 2L,
                                                    3L, 1L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 2L, 3L, 2L, 1L, 3L, 1L,
                                                    3L, 3L, 1L, 2L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
                                                    3L, 3L, 2L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 2L, 1L,
                                                    3L, 3L, 3L, 1L, 3L, 1L, 2L, 3L, 2L, 2L, 2L, 1L, 2L, 2L, 3L,
                                                    1L, 3L, 3L, 3L, 2L, 1L, 2L, 1L, 1L, 3L, 3L, 3L, 1L, 3L, 3L,
                                                    1L, 1L, 2L, 3L, 1L, 2L, 2L, 3L, 2L, 3L, 2L, 3L, 3L, 2L, 2L,
                                                    3L, 1L, 1L, 2L, 1L, 2L, 3L, 1L, 2L, 2L, 1L, 2L, 3L, 1L, 1L,
                                                    1L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 2L, 3L,
                                                    2L, 2L, 1L, 3L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 3L, 2L, 3L, 1L,
                                                    2L, 2L, 2L, 3L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
                                                    3L, 3L, 2L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 3L, 2L,
                                                    1L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 2L, 2L, 3L, 2L, 3L, 1L, 2L,
                                                    3L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L,
                                                    3L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 3L, 3L, 2L, 1L, 2L, 3L,
                                                    1L, 1L, 2L, 3L, 1L, 2L, 3L, 3L, 3L, 1L, 3L, 1L, 2L, 3L, 3L,
                                                    1L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 2L, 2L, 1L, 2L, 3L, 2L, 2L,
                                                    1L, 2L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 3L, 1L, 3L, 1L, 1L, 2L,
                                                    2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 3L, 1L,
                                                    1L, 1L, 3L, 1L, 2L, 3L, 3L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 1L,
                                                    1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 3L, 3L, 1L, 3L, 3L, 3L, 3L,
                                                    3L, 1L, 1L, 1L, 1L, 3L, 3L, 2L, 1L, 2L, 2L, 3L, 3L, 1L, 3L,
                                                    1L, 3L, 2L, 1L, 1L, 1L, 3L, 3L, 1L, 2L, 1L, 2L, 3L, 1L, 1L,
                                                    1L, 2L, 1L, 2L, 1L, 1L, 3L, 1L, 2L, 2L, 3L, 1L, 1L, 1L, 1L,
                                                    1L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 3L, 1L, 3L, 1L, 1L, 1L,
                                                    1L, 2L, 3L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 3L, 2L, 1L,
                                                    1L, 1L, 1L, 3L, 3L, 1L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 2L,
                                                    1L, 1L, 3L, 1L, 1L, 1L, 2L, 3L, 1L, 2L, 2L, 2L, 1L, 3L, 1L,
                                                    3L, 1L, 3L, 3L, 3L, 1L, 2L, 3L, 1L, 3L, 3L, 1L, 1L, 2L, 3L,
                                                    2L, 2L, 1L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 2L, 2L, 3L, 1L, 3L,
                                                    1L, 3L, 3L, 3L, 2L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 3L, 3L,
                                                    2L, 3L, 3L, 1L, 1L, 2L, 1L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 1L,
                                                    3L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 2L, 3L, 3L,
                                                    2L, 3L, 2L, 3L, 2L, 2L, 3L, 1L, 3L, 1L, 2L, 2L, 1L, 3L, 1L,
                                                    3L, 3L, 1L, 3L, 2L, 3L, 2L, 1L, 2L, 1L, 1L, 3L, 3L, 3L, 1L,
                                                    1L, 2L, 3L, 2L, 2L, 3L, 1L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 2L,
                                                    2L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, 1L, 3L, 3L, 2L, 3L, 3L,
                                                    3L, 3L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L,
                                                    3L, 2L, 3L, 1L, 3L, 1L, 1L, 3L, 3L, 1L, 3L, 2L, 1L, 2L, 1L,
                                                    1L, 1L, 3L, 1L, 1L, 2L, 2L, 1L, 3L, 3L, 3L, 3L, 3L, 1L, 1L,
                                                    3L, 2L, 1L, 1L, 1L, 3L, 1L, 3L, 3L, 1L, 3L, 1L, 2L, 2L, 1L,
                                                    3L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 3L, 1L, 2L, 1L, 3L, 3L, 1L,
                                                    3L, 1L, 3L, 3L, 3L, 2L, 3L, 3L, 3L, 2L, 2L, 1L, 1L, 1L, 1L,
                                                    3L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 3L, 2L, 1L, 3L, 2L, 2L, 1L,
                                                    1L, 2L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 2L, 3L, 2L, 1L,
                                                    2L, 2L, 2L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
                                                    1L, 1L, 1L, 3L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 1L,
                                                    2L, 2L, 3L, 1L, 1L, 3L, 3L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 3L,
                                                    3L, 3L, 1L, 3L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 2L, 2L, 3L, 3L,
                                                    3L, 3L, 1L, 3L, 2L, 3L, 1L, 3L, 3L, 2L, 1L, 3L, 3L, 2L, 3L,
                                                    1L, 2L, 2L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 3L, 3L, 1L, 3L, 3L,
                                                    1L, 3L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 3L, 1L, 2L,
                                                    3L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L,
                                                    2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 3L, 3L, 1L, 3L,
                                                    1L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 2L, 3L, 1L, 3L, 1L, 3L, 3L,
                                                    2L, 1L, 2L, 1L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 2L,
                                                    1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 1L, 1L,
                                                    1L, 2L, 1L, 1L, 1L, 3L, 2L, 1L, 3L, 1L, 1L, 1L, 2L, 2L, 3L,
                                                    1L, 1L, 3L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 3L,
                                                    1L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 3L, 2L,
                                                    3L, 1L, 2L, 3L, 1L, 3L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 1L, 3L,
                                                    1L, 3L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 1L,
                                                    3L, 1L, 2L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 2L, 3L, 1L, 1L,
                                                    2L, 1L, 3L, 2L, 2L, 3L, 2L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 1L,
                                                    3L, 2L, 3L, 1L, 3L, 1L, 1L, 2L, 2L, 3L, 1L, 1L, 1L, 1L, 1L,
                                                    1L, 1L, 3L, 3L, 3L, 3L, 1L, 3L, 2L, 1L, 1L, 1L, 2L, 1L, 2L,
                                                    3L, 1L, 2L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 1L,
                                                    3L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 3L, 3L, 2L, 1L, 3L,
                                                    1L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 1L,
                                                    1L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 1L, 3L,
                                                    2L, 3L, 3L, 3L, 1L, 3L, 1L, 3L, 3L, 2L, 1L, 1L, 3L, 3L, 1L,
                                                    3L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 2L, 1L,
                                                    3L, 1L, 2L, 3L, 3L, 1L, 2L, 2L, 1L, 3L, 3L, 3L, 1L, 1L, 2L,
                                                    3L, 1L, 1L, 3L, 3L, 3L, 2L, 2L, 2L, 2L, 3L, 2L, 2L, 1L, 1L,
                                                    1L, 1L, 2L, 1L, 3L, 1L, 3L, 3L, 1L, 3L, 3L, 1L, 1L, 3L, 1L,
                                                    1L, 3L, 2L, 1L, 1L, 1L, 2L, 2L, 3L, 3L, 3L, 3L, 2L, 1L, 2L,
                                                    1L, 1L, 1L, 3L, 1L, 2L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 3L,
                                                    3L, 2L, 3L, 1L, 1L, 3L, 3L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 3L,
                                                    2L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 1L, 3L, 3L, 1L, 3L, 3L, 3L,
                                                    1L, 1L, 1L, 3L, 3L, 2L, 1L, 2L, 3L, 3L, 3L, 2L, 3L, 3L, 1L,
                                                    3L, 1L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 3L, 1L, 1L, 3L, 3L, 3L,
                                                    1L, 3L, 2L, 3L, 3L, 1L, 1L, 3L, 1L, 2L, 2L, 1L, 1L, 1L, 3L,
                                                    1L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 3L, 1L, 2L, 3L, 2L, 1L,
                                                    1L, 3L, 1L, 2L, 2L, 1L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 3L, 1L,
                                                    3L, 2L, 3L, 1L, 3L, 1L, 1L, 3L, 1L, 2L, 1L, 3L, 3L, 1L, 1L,
                                                    3L, 2L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 2L, 1L, 3L, 2L, 1L, 2L,
                                                    1L, 1L, 2L, 3L, 1L, 1L, 2L, 3L, 1L, 1L, 3L, 3L, 2L, 1L, 1L,
                                                    3L, 2L, 2L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, 1L, 1L, 3L, 3L, 1L,
                                                    1L, 1L, 1L, 3L, 2L, 2L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 3L, 1L,
                                                    2L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 2L, 3L, 2L, 2L, 2L, 1L,
                                                    2L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 2L, 3L, 3L, 1L, 1L,
                                                    1L, 1L, 3L, 3L, 1L, 3L, 3L, 2L, 3L, 2L, 3L, 1L, 3L, 3L, 1L,
                                                    1L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 2L, 1L,
                                                    1L, 1L, 1L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
                                                    1L, 3L, 3L, 1L, 1L, 3L, 3L, 1L, 1L, 3L, 3L, 3L, 3L, 1L, 2L,
                                                    1L, 1L, 3L, 3L, 2L, 1L, 3L, 3L, 1L, 2L, 3L, 1L, 1L, 2L, 3L,
                                                    3L, 3L, 1L, 2L, 3L, 3L, 3L, 2L, 1L, 3L, 1L, 1L, 3L, 3L, 3L,
                                                    1L, 1L, 1L, 3L, 3L, 2L, 1L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L,
                                                    3L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 3L, 3L, 3L,
                                                    3L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 3L, 3L, 3L, 3L, 1L, 3L, 3L,
                                                    3L, 3L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 3L, 3L,
                                                    3L, 1L, 3L, 2L, 3L, 3L, 1L, 3L, 2L, 3L, 3L, 1L, 1L, 1L, 3L,
                                                    3L, 3L, 3L, 1L, 3L, 2L, 1L, 2L, 2L, 1L, 3L, 3L, 1L, 1L, 1L,
                                                    3L, 3L, 1L, 2L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 1L, 1L,
                                                    1L), class = "factor", .Label = c("No", "No internet service",
                                                                                      "Yes"), questiontype = "PickOne", name = "OnlineBackup_cat", label = "OnlineBackup", question = "OnlineBackup"),
                     stringsAsFActors = c(FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
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                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
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                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
                                          FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE)), class = "data.frame", row.names = c(NA,
                                                                                                                                        -7043L))
test_that("Multiple imputation with larger example",
{
    expect_warning(Regression(Churn_cat~OnlineSecurity_cat + OnlineBackup_cat, type = "Binary Logit", data = df, missing = "Multiple imputation"))})


test_that("R4.0. update", {
    expect_warning(Regression(Overall~Fees+Interest+Phone, data=bank, interaction = ATM, type = "NBD", missing = "Multiple imputation"))
})