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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
import java.util.Arrays;
import java.util.TreeSet;

public class Main{
  static final int INF = Integer.MAX_VALUE / 2;
  static int n;
  static int[] a;

  static final boolean DEBUG = false;

  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    n = sc.nextInt();

    a = new int[3 * n];
    for(int i = 0; i < 3 * n; i++){
      a[i] = sc.nextInt();
    }

    int[] b = new int[3 * n];
    for(int i = 0; i < 3 * n; i++){
      b[i] = a[3 * n - i - 1];
    }

    long[] dp1 = new long[3 * n + 1];
    int min = INF;
    TreeSet< Integer > s1 = new TreeSet< >();
    for(int i = 0; i < n; i++){
      min = Math.min(min, a[i]);
      dp1[n] += a[i];
      s1.add(a[i]);
    }
    for(int i = n + 1; i <= 3 * n; i++){
      s1.add(a[i - 1]);
      if(a[i - 1] > min){
        dp1[i] = dp1[i - 1] - min + a[i - 1];
        if(s1.higher(min) != null){
          min = s1.higher(min);
        }
      }
      else{
        dp1[i] = dp1[i - 1];
      }
    }

    long[] dp2 = new long[3 * n + 1];
    int max = 0;
    TreeSet< Integer > s2 = new TreeSet< >();
    for(int i = 0; i < n; i++){
      max = Math.max(max, b[i]);
      dp2[n] += b[i];
      s2.add(b[i]);
    }
    for(int i = n + 1; i <= 3 * n; i++){
      s2.add(b[i - 1]);
      if(b[i - 1] < max){
        dp2[i] = dp2[i - 1] - max + b[i - 1];
        if(s2.lower(max) != null){
          max = s2.lower(max);
        }
      }
      else{
        dp2[i] = dp2[i - 1];
      }
    }

    if(DEBUG){
      for(int i = n; i <= 3 * n; i++){
        System.out.println("dp1[" + i + "] = " + dp1[i]);
      }
      for(int i = n; i <= 3 * n; i++){
        System.out.println("dp2[" + i + "] = " + dp2[i]);
      }
    }

    long ans = Long.MIN_VALUE / 2;
    for(int i = n; i <= 2 * n; i++){
      ans = Math.max(ans, dp1[i] - dp2[3 * n - i]);
      if(DEBUG){
        System.out.println("i = " + i);
        System.out.println("3 * n - i = " + (3 * n - i));
        System.out.println(dp1[i] - dp2[3 * n - i]);
      }
    }

    System.out.println(ans);
  }
}