import Data.Ratio

main :: IO ()
main = mapM_ printIntersection ls
  where
    ls =
      [
        (line (0, 8) (4, 0), line (2, 4) (8, 12))
      , (line (0, 0) (1, 2), line (1, 1) (2, 3))
      , (line (-9, -9) (1, 1), line (5, 0) (5, 3))
      , (line (3, 4) (6, 7), line (3, 8) (9, -1))
      ]

printIntersection :: (Line, Line) -> IO ()
printIntersection (l, m) = putStrLn s
  where
    s | any isNaN [x, y] = "交点なし"
      | otherwise        = show (x, y)
    (x, y) = intersection l m

type Point = (Double, Double)
type Line  = (Ratio Integer, Ratio Integer, Ratio Integer)

line :: Point -> Point -> Line
line (x1, y1) (x2, y2)
  | dx /= 0   = (toRational slope, - 1, toRational $ slope * x1 - y1)
  | dx == 0   = (1, 0, toRational x1)
  | otherwise = (0, 0, toRational x1)
  where
    slope = dy / dx
    dx = x2 - x1
    dy = y2 - y1

intersection :: Line -> Line -> Point
intersection l@(a, b, p) m@(c, d, q)
  | not $ parallel l m = (fromRational x, fromRational y)
  | otherwise          = (nan, nan)
  where
    x = invd * p + invb * q
    y
      | 0 `elem` [a, b] = c * x + q
      | 0 `elem` [c, d] = a * x + p
      | otherwise       = invc * p + inva * q
    [inva, invb, invc, invd] = map (/ det l m) [a, -b, -c, d]
    nan :: Double
    nan = 0 / 0

parallel :: Line -> Line -> Bool
parallel l m = det l m == (0 % 1)

det :: Line -> Line -> Ratio Integer
det (a, b, _) (c, d, _) = a * d - b * c