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: Time Limit Exceeded)

import Data.List
import Data.Maybe
import qualified Data.IntMap.Strict as M
import qualified Data.ByteString.Char8 as B
 
readInt = fst . fromJust . B.readInt

apply n f x = foldr ($) x (replicate n f)
 
main = do
 n <- readLn
 as <- map readInt . B.words <$> B.getLine
 let (as1,as2) = splitAt n as
 let q1 = M.fromListWith (+) (zip as1 (repeat 1))
 let q2 = M.fromListWith (+) (zip as2 (repeat 1))
 print (n3 n q1 as2 q2)
 
n3 n q1 as2 q2 = maximum (fsearch n q1 as2 q2)
 
fsearch n q1 as q2 = do
 k <- [0..n]
 let (rh,rl) = transfer (n-k) k q1 as q2
 return (rh - rl)

pred' v = if v > 1 then Just (pred v) else Nothing

transfer n' 0 q1 _ q2 = (sumq q1, sumq (apply n' (M.updateMax pred') q2))
 where sumq = sum . map (uncurry (*)) . M.toList
 
transfer n' k q1 (a:as) q2 = transfer n' (k-1) (M.insertWith (+) a 1 q1') as q2'
 where
  q1' = M.updateMin pred' q1
  q2' = M.update pred' a q2