import "prelude.eg"

namespace Hailstone (

    using System
    using List

    def even = [ N -> (N%2) == 0 ]

    def hailstone =
        [ 1 -> {1}
        | N -> if even N then cons N (hailstone (N/2))
               else cons N (hailstone (N * 3 + 1)) ]

    def hailpair =
        [ N -> (N, length (hailstone N)) ]

    def hailmax =
        [ (N, NMAX), (M, MMAX) -> if (NMAX < MMAX) then (M, MMAX) else (N, NMAX) ]

    def largest =
        [ 1 -> (1, 1)
        | N ->
            let M0 = hailpair N in
            let M1 = largest (N - 1) in
                hailmax M0 M1 ]
)

using System
using List
using Hailstone

def task0 = let H27 = hailstone 27 in length H27

def task1 =
    let H27 = hailstone 27 in
    let L   = length H27 in
        (take 4 H27, drop (L - 4) H27)

def task2 = largest 100000

def main = (task0, task1, task2)