module Main where

import           Data.List
import           Data.Matrix
import           System.Environment

main :: IO ()
main = do
  args <- getArgs
  let n = read $ head args :: Int
    in putStrLn $ intercalate "\n" $ map show $ solve n

data Square = O | X | Qu deriving (Show, Eq)

solve :: (Eq n, Num n) => n -> [Matrix Square]
solve n = nub $ solveN n
  where
    solveN 1 = solve' [initBoard]
    solveN x = solve' (solveN (x-1))
    solve' bs = concatMap (\bn -> map ((`placeQueen` bn)) (openPositions bn)) bs

initBoard :: Matrix Square
initBoard = matrix 8 8 (const O)

placeQueen :: (Int, Int) -> Matrix Square -> Matrix Square
placeQueen p b = setElem Qu p $ markAttacks p b

markAttacks :: (Int, Int) -> Matrix Square -> Matrix Square
markAttacks p b = markAll positions b
  where markAll [] mb = mb
        markAll (mp:mps) mb = let nb = setElem X mp mb
                              in markAll mps nb
        positions  = concatMap walk stepDirections
          where walk dir = takeWhile inBounds $ iterate (dir) $ dir p
                inBounds (i,j) = i >= 1 && i <= nrows b &&
                                 j >= 1 && j <= ncols b
                stepDirections =
                  let a = (+1); s = subtract 1; k = id -- add; subtract; keep
                      dirF (fr,fc) = (\(r,c) -> (fr r, fc c))
                  in map dirF [   (a,k), (s,k)              -- up, down
                                , (k,a),(k,s)               -- right, left
                                , (a,a),(a,s),(s,a),(s,s) ] -- diagonals

openPositions :: Matrix Square -> [(Int, Int)]
openPositions b = [(r,c) | r <- [1..8], c <- [1..8], b ! (r,c) == O ]