type Perm = [Int]
data Parity = Odd | Even deriving Show

oddtest = [1,3,2,4,5] :: Perm
eventest = [1,4,2,3,5] :: Perm

genPairs :: Int -> [(Int, Int)]
genPairs l = [(a,b) | a <- [1..l], b <- [1..l], a < b]


inversion :: Perm -> (Int,Int) -> Bool
inversion p (x,y) = o x > o y
    where
      o a = p !! (a-1)


countInversions p = length $ filter id $ map (inversion p) $ genPairs $ length p

parity :: Perm -> Parity
parity p | even $ countInversions p = Even
         | otherwise = Odd