module Main

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

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 s n [e:ee]
  | e > s = []
  = map ((:>) e) (comb_sum (s - e) ck ee) // <- この部分を修正
  where
  ck = reverse $ take (n-1) $ scan (+) 0 $ reverse $ ee
  comb_sum 0 [] _ = [[]]
  comb_sum _ [] _ = []
  comb_sum _ _ [] = []
  comb_sum s ck=:[c:cc] [e:ee]
    | e > s     = []
    | e < s - c = comb_sum s ck ee
                = map ((:>) e) (comb_sum (s-e) cc ee) ++ comb_sum s ck ee