{- queens9.out, as produced by this program, is 32032 bytes -}

main = writeQueens 9

writeQueens n = writeFile fn (show (queens n))
    where
      fn = "queens" ++ show n ++ ".out"

newtype Queens = Queens [[Int]]

instance Show Queens where
    show (Queens qs) = concatMap showBoard qs

showBoard board = concatMap showRow board ++ "\n"
    where
      size = length board
      dots = replicate size '.'
      showRow n = take (n - 1) dots ++ "X" ++ take (size - n) dots ++ "\n"

queens b = Queens (queens' b)
    where
      queens' 0 = [[]]
      queens' n = [ p ++ [n] | p <- queens' (n - 1), n <- [1..b], safe p n ]

safe p n = and [ not (check (i, j) (m, n)) | (i, j) <- zip [1 .. l] p]
    where l = length p; m = l + 1

check (i, j) (m, n) = j == n || i + j == m + n || i - j == m - n