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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.PriorityQueue
import java.util.Comparator

object MainKt {
  @JvmStatic fun main(args:Array<String>) {
    val N=readLine()!!.toInt()
    val a=readLine()!!.split(" ").map(String::toInt)
    assert(a.size==N)
    
    val default_front_queue = PriorityQueue<Int>()
    val default_last_queue=PriorityQueue<Int>(N,object: Comparator<Int> {
      override fun compare(a:Int,b:Int) = b-a
    })
    
    var default_front_acc=0L
    var default_last_acc=0L
 
    a.slice(0.until(N)).forEach{
          default_front_acc+=it
          default_front_queue.add(it)
          }
       a.slice((2*N).until(3*N)).forEach{ 
         default_last_acc+=it
         default_last_queue.add(it)
         }

    println(
      if(N==1) {
        arrayOf(a[0]-a.slice(1..2).max()!!,a.slice(0..1).max()!!-a[2]).max()!!
      }
      else {
          ((N-1).until(2*N)).fold(0L) {res,k->
          
          val front_queue=default_front_queue
          var front_acc=default_front_acc
          val last_queue=default_last_queue
          var last_acc=default_last_acc
          
          for(i in N..k) {
            front_queue.add(a[i])
            front_acc+=a[i]
            front_acc-=front_queue.poll()
          }
          for(i in (k+1).until(2*N)) {
            last_queue.add(a[i])
            last_acc+=a[i]
            last_acc-=last_queue.poll()        
          }
          //  println(k)
          //  println(front_queue)
          //  println(last_queue)
          if(front_acc-last_acc > res) {front_acc-last_acc} else {res}
        }
      })
  }
}