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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include "bits/stdc++.h"
using namespace std;

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)   FOR(i,0,n)
#define LL long long

LL a[300000],l[100001],r[100001];
int n;

int main(){
  cin>>n;
  REP(i,3*n)
    cin>>a[i];

  LL su=accumulate(a,a+n,0);
  priority_queue<LL,vector<LL>,greater<LL>> q;
  REP(i,n)
    q.push(a[i]);
  REP(i,n+1){
    l[i]=su;
    q.push(a[n+i]);
    su+=a[n+i]-q.top();
    q.pop();
  }

  su=accumulate(a+2*n,a+3*n,0);
  priority_queue<LL> q2;
  REP(i,n)
    q2.push(a[2*n+i]);
  REP(i,n+1){
    r[n-i]=su;
    q2.push(a[2*n-1-i]);
    su+=a[2*n-1-i]-q2.top();
    q2.pop();
  }
  
  LL ret=-1e15;
  REP(i,n+1){
    //cerr<<i<<" "<<l[i]<<" "<<r[i]<<endl;
    ret=max(ret,l[i]-r[i]);
  }
  cout<<ret<<endl;
  return 0;
}