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 Scala (2.11.7) (judge verdict: Wrong Answer)

object Main extends App {
  import collection.mutable.PriorityQueue
  val sc = new java.util.Scanner(System.in)
  val N = sc.nextInt
  val As = Array.fill(3*N)(sc.nextInt)

  def f(xs: Array[Int], ys: Array[Int]): Array[Int] = {
    val pq = new PriorityQueue[Int]()(Ordering.Int.reverse) ++ xs
    ys.scanLeft(pq.sum) { (s, y) =>
      pq += y
      s + y - pq.dequeue}
  }

  val List(as1, as2, as3) = As.grouped(N).toList
  val ans = f(as1, as2).zip(f(as3.map(a => -a), as2.map(a => -a).reverse).reverse).map(t => t._1 + t._2).max
  println(ans)
}