groups.hs

-- Make: ghc --make groups.hs
-- Run: echo -e "[4,3,3,2]\n[5,3,2,1,1,3,5]\n[4,5]" | ./groups
import System.IO
import Data.List

isSameSolution f (s1,s2)   = f == (s2,s1)
discardDuplicated          = nubBy isSameSolution
uniqueSubsequences         = filter ((/=0).length) . nub . subsequences

solutionsFor list          = discardDuplicated solutions
  where solutions          = [(x,y) | x <- subsequencesOfList, y <- listWithout x, sum x == sum y]
        subsequencesOfList = uniqueSubsequences list
        listWithout x      = [list \\ x]

output []       = "no solution\n"
output solution = unlines $ map show solution

main = do
  theEnd <- isEOF
  if theEnd
    then return ()
    else do line <- getLine
            putStr $ output $ solutionsFor (read line :: [Int])
            main