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: Accepted)

import java.io.{BufferedReader, InputStream, InputStreamReader}
import java.util.StringTokenizer

import scala.collection.mutable
import scala.util.Sorting
import math.{abs, max, min}

object Main {
  val MOD = 1000000007
  def solve(): Unit = {
    val sc = new InputReader(System.in)
    val N = sc.nextInt()

    var L: Long = 0
    val left = mutable.PriorityQueue[Long]()(Ordering[Long].reverse)
    (0 until N) foreach { _ =>
      val a = sc.nextLong()
      left.enqueue(a)
      L += a
    }

    val mid = Array.fill[Long](N)(sc.nextLong())

    var R: Long = 0
    val right = mutable.PriorityQueue[Long]()
    (0 until N) foreach { _ =>
      val a = sc.nextLong()
      right.enqueue(a)
      R += a
    }

    val dL = Array.ofDim[Long](N + 1)
    dL(0) = L
    val dR = Array.ofDim[Long](N + 1)
    dR(N) = R

    (0 until N) foreach { i =>
      val add = mid(i)
      left.enqueue(add)
      val remove = left.dequeue()
      dL(i + 1) = dL(i) + add - remove
    }

    (0 until N) foreach { j =>
      val i = N - 1 - j
      val add = mid(i)
      right.enqueue(add)
      val remove = right.dequeue()
      dR(i) = dR(i + 1) + add - remove
    }

    val ans = (dL zip dR map { case (l, r) => l - r }).max

    println(ans)
  }


  def main(args: Array[String]): Unit = {
    solve()
  }


  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = null

    def next: String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next.toInt
    def nextLong(): Long = next.toLong
    def nextChar(): Char = next.charAt(0)
  }

}