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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
static int n = int.Parse(Console.ReadLine());//int.Parseは文字列を整数に変換。
static long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
static long[] numsThree = new long[n];//和に使うリスト
static long[] numsThreeR = new long[n];
static long[] sum = new long[n+1];
static long[] sumR = new long[n+1];
static long answer = 0;

	static void Main()
	{
    for(int i=0; i<n; i++)
    {
    sum[0] += nums[i];
    numsThree[i] = nums[i];
    
    sumR[n] += nums[3*n-1-i];
    numsThreeR[i] = nums[3*n-1-i];
    }
    Array.Sort(numsThree);//昇順にソート
    Array.Sort(numsThreeR);

    for(int i=0; i<n; i++)
    {
      ListChange(nums[n+i],i);
      ListChangeR(nums[2*n-1-i],i);
    }

    for(int i=0; i<=n; i++)
    {
      long ans = sum[i] - sumR[i];
      Console.WriteLine(sum[i] +" "+ sumR[i]);//デバッグ
      if(ans > answer) answer = ans;
    }
    
	Console.WriteLine(answer);
	}

  static void ListChange(long changeNum, int i)//二分探索によるリストの変更
  {
    int min = 0;
    int max = numsThree.Length - 1;

      while (true)
      {
      if(changeNum <= numsThree[0]) break;
      int mid = min + (max - min) / 2;
      if(changeNum > numsThree[mid]) min = mid;
      else max = mid;

        if(max - min <= 1)
        {
          if(changeNum >= numsThree[min] && changeNum <= numsThree[max]) 
          {
            sum[i+1] = sum[i] - numsThree[min];
            numsThree[min] = changeNum;
            sum[i+1] = sum[i] + changeNum;
          }
          else if(changeNum > numsThree[max]) 
          {
            sum[i+1] = sum[i] - numsThree[max];
            numsThree[max] = changeNum;
            sum[i+1] = sum[i] + changeNum;
          }
          else if(changeNum < numsThree[min]) 
          {
            sum[i+1] = sum[i] - numsThree[min];
            numsThree[min] = changeNum;
            sum[i+1] = sum[i] + changeNum;
          }
          break;
        }
    
      }
    
  }

  static void ListChangeR(long changeNum, int i)//二分探索によるリストの変更
  {
    int min = 0;
    int max = numsThreeR.Length - 1;

      while (true)
      {
      if(changeNum >= numsThree[max]) break;
      int mid = min + (max - min) / 2;
      if(changeNum > numsThreeR[mid]) min = mid;
      else max = mid;

        if(max - min <= 1)
        {
          if(changeNum >= numsThreeR[min] && changeNum <= numsThree[max]) 
          {
            sumR[i+1] = sumR[i] - numsThree[max];
            numsThreeR[max] = changeNum;
            sumR[i+1] = sumR[i] + changeNum;
          }
          else if(changeNum < numsThreeR[min])
          {
            sum[i+1] = sum[i] - numsThree[min];
            numsThree[min] = changeNum;
            sum[i+1] = sum[i] + changeNum;
          }
          else if(changeNum > numsThreeR[max])
          {
            sum[i+1] = sum[i] - numsThree[max];
            numsThree[max] = changeNum;
            sum[i+1] = sum[i] + changeNum;
          }
          break;
        }
    
      }
    
  }
  
}