main :: IO ()
main = readFile "2/input.txt" >>= print . solve . parse . lines

parse :: [String] -> [Instruction]
parse = map (parseLine . words)

solve :: [Instruction] -> (Int,Int)
solve input = (f input, g input)
    where f = uncurry (*) . simulate Abs
          g = uncurry (*) . simulate (Aim 0)

data Nav = Aim Int 
         | Abs

data Instruction = Forward Int
                 | Down Int
                 | Up Int

parseLine :: [String] -> Instruction
parseLine [ s, x ]
    | s == "forward" = Forward n
    | s == "down"    = Down n
    | s == "up"      = Up n
    where
        n = read x

simulate :: Nav -> [Instruction] -> (Int,Int)
simulate nav = iter nav (0,0)

iter :: Nav -> (Int,Int) -> [Instruction] -> (Int,Int)
iter _ r [] = r
iter Abs (x,y) (i:is) = case i of
        Forward n -> iter Abs (x+n,y)
        Down n    -> iter Abs (x,y+n)
        Up n      -> iter Abs (x,y-n)
    $ is
iter (Aim a) (x,y) (i:is) = case i of
        Forward n -> iter (Aim a) (x+n,y+(a*n))
        Down n    -> iter (Aim (a+n)) (x,y)
        Up n      -> iter (Aim (a-n)) (x,y)
    $ is