Quick, reliable pseudo-shuffler (enhanced)

import Data.Function
import Data.List

orderLists :: [a] -> [a] -> ([a], [a])
orderLists xs ys
  | on compare length xs ys == LT = (xs, ys)
  | otherwise = (ys, xs)

listsLengthQuotient :: ([a], [a]) -> ([a], [a], Int)
listsLengthQuotient (xs, ys) =
  (xs, ys, (round $ on (/) (fromIntegral . length) ys xs) :: Int)

chunksOf :: Int -> [a] -> [[a]]
chunksOf n [] = []
chunksOf x xs = take x xs : chunksOf x (drop x xs)

groupListItems :: ([a], [a], Int) -> ([[a]], [[a]])
groupListItems (xs, ys, q) = (chunksOf 1 xs, chunksOf q ys)

merge :: ([a], [a]) -> [a]
merge (xs, []) = xs
merge ([], ys) = ys
merge (x:xs, y:ys) = y : x : merge (xs, ys)

mixLists :: [a] -> [a] -> [a]
mixLists xs ys =
  concat $ merge $ groupListItems $ listsLengthQuotient $ orderLists xs ys

main :: IO ()
main = do
  input <- getContents
  mapM_ putStrLn $
    foldl1 mixLists $ sortBy (on compare length) (group . sort $ lines input)