import Data.List ( permutations )

symmetric :: Int -> [[Int]]
symmetric n = permutations [1..n]

inversions :: Int -> [Int] -> Int
inversions n [] = n
inversions n (x:[]) = n
inversions n (x:xs) = inversions (n+m) xs
  where
    -- is x greater than values in xs?
    gs :: [Bool]
    gs = fmap (x >) xs

    -- number of times x is greater
    m :: Int
    m = (sum . fmap fromEnum) gs

countInversions :: [Int] -> Int
countInversions xs = inversions 0 xs

main :: IO ()
main = print $ filter (even . countInversions) (symmetric 3)