import Data.Ratio

main :: IO ()
main = mapM_ printIntersection ls
  where
    ls =
      [
        (((0, 8), (4, 0)), ((2, 4), (8, 12)))
      , (((0, 0), (4, 6)), ((0, 0), (7, 15)))
      , (((0, 0), (1, 2)), ((1, 1), (2, 3)))
      , (((-9, -9), (9, 9)), ((5, 0), (5, 7)))
      , (((3, 4), (6, 7)), ((3, 8), (9, -1)))
      , (((-1, 0), (4, 18)), ((-2, -5), (1, 3)))
      ]

printIntersection :: ((Point, Point), (Point, Point)) -> IO ()
printIntersection (l, m) = putStrLn s
  where
    s =
     if not (onSegment l && onSegment m) || any isNaN [x, y] then
       "交点なし"
     else
       show (x, y)
    (x, y) = intersection (uncurry line l) (uncurry line m)

    onSegment ((x1, y1), (x2, y2)) = checkX && checkY
      where
        checkX = cmp (if x1 <= x2 then (<=) else (>=)) [x1, x, x2]
        checkY = cmp (if y1 <= y2 then (<=) else (>=)) [y1, y, y2]
        cmp f = and . (flip (zipWith f) =<< tail)


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, 0)
  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 == a    = c * x + q
      | 0 == c    = 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