Problem:
Score : 500 points

Problem Statement

Let N be a positive integer.

There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}).
Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.
Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').

Find the maximum possible score of a'.

Constraints

1 ≤ N ≤ 10^5

a_i is an integer.

1 ≤ a_i ≤ 10^9

Partial Score

In the test set worth 300 points, N ≤ 1000.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{3N}

Output

Print the maximum possible score of a'.

Sample Input 1

2
3 1 4 1 5 9

Sample Output 1

1

When a_2 and a_6 are removed, a' will be (3, 4, 1, 5), which has a score of (3 + 4) - (1 + 5) = 1.

Sample Input 2

1
1 2 3

Sample Output 2

-1

For example, when a_1 are removed, a' will be (2, 3), which has a score of 2 - 3 = -1.

Sample Input 3

3
8 2 2 7 4 6 5 3 8

Sample Output 3

5

For example, when a_2, a_3 and a_9 are removed, a' will be (8, 7, 4, 6, 5, 3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5.

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

{-# LANGUAGE BangPatterns #-}
import Control.Arrow
import Control.Monad
import Control.Monad.Fix
import Data.Int
import Data.Foldable
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.Set as S
import qualified Data.ByteString.Char8 as B
import Debug.Trace

solve :: Int -> VU.Vector Int -> Int
solve !n !an = maximum $ zipWith
  (+)
  (take n $ drop (n + 1) calcSumAs)
  (take n $ drop (n + 1) $ reverse calcSumBs)
 where
  ain = VU.imap (\(!i) (!a) -> (a, i)) an
  calc an = (\(_, _, !x) -> x) $ VU.foldl'
    (\(!heap, !s, !acc) (!ai, !i) ->
      let heap'        = S.insert (ai, i) heap
          (s', heap'') = if S.size heap' > n
            then
              let Just ((m, _), heap'') = S.minView heap'
              in  (s + ai - m, heap'')
            else (s + ai, heap')
      in  (heap'', s', s' : acc)
    )
    (S.empty, 0, [0])
    an

  calcSumAs = calc ain
  calcSumBs = calc $ VU.map (\(!ai, !i) -> (-ai, i)) $ VU.reverse ain

main = do
  let readInt :: Integral a => B.ByteString -> Maybe (a, B.ByteString)
      readInt = fmap (first fromIntegral . second B.tail) . B.readInt

  n  <- (\vec -> (vec VU.! 0)) . VU.unfoldrN 1 readInt <$> B.getLine
  an <- VU.unfoldrN (3 * n) readInt <$> B.getLine
  print $ solve n an