DouKaku?

module Main

import Bool, Int, List, Array, ValueCast, StringCast, System, Misc

Start = length $
        divide n s ls
  where
  n = toInt getCommandLine.[1]
  ls = [1..n*n]
  s = sum ls / n

divide n s ls = search ls
  where
  search [] = [[]]
  search ls
    =  comb_sum s n ls
    |> map (\f = let
                   (f0,fr) = (head f, tail f)
                   rr = filter (\e = not (e <= f0 || fr contains e)) ls
                 in [[f:t] \\ t <- search rr])
    |> foldr (++) []

comb_sum :: Int Int [Int] -> [[Int]]
comb_sum 0 0 _ = [[]]
comb_sum _ 0 _ = []
comb_sum s _ [] = []
comb_sum s n [e:rr]
  | e > s
    = comb_sum s n rr
    = map ((:>) e) (comb_sum (s-e) (n-1) rr) ++ comb_sum s n rr

/*
  //1. filterの部分をrest_of関数で置き換え
  search [] = [[]]
  search ls
    =  comb_sum s n ls
    |> map (\f = let rr = rest_of f ls
                 in [[f:t] \\ t <- search rr])
    |> foldr (++) []

  rest_of _ [] = []
  rest_of es=:[e:ee] ls=:[l:ll]
    | l <= e = rest_of es ll
    = rm ee ls
    where
    rm _ [] = []
    rm [] ls = ls
    rm es=:[e:ee] ls=:[l:ll]
      | l < e  = [l: rm es ll]
      | e == l = rm es ll
               = rm ee ls

  //2. searchで直接グループわけの個数を計算
  search [] = 1
  search ls
    =  comb_sum s n ls
    |> map (\f = let rr = rest_of f ls
                 in search rr)
    |> sum
*/