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 <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;

const int maxn=1e5+5;
int arr[maxn*3],n;

int check(int mid)
{
    //printf("%d\n",mid);
    int a[maxn*3];
    for(int i=0;i<3*n;++i) a[i]=arr[i];
    int lans=0,rans=0;
    sort(a,a+mid);
    sort(a+mid,a+3*n);
    //for(int i=0;i<3*n;++i) printf("%d%c",a[i],i==3*n-1?'\n':' ');
    for(int i=mid-1;i>=mid-n;--i) lans+=a[i];
    for(int i=mid;i<mid+n;++i) rans+=a[i];
    //printf("%d %d\n",lans,rans);
    return lans-rans;
}

int main()
{
    while(~scanf("%d",&n))
    {
        for(int i=0;i<3*n;++i)
            scanf("%d",&arr[i]);
        int l=n,r=2*n;
        while(l+2<r)
        {
            //printf("%d %d\n",l,r);
            int lmid=l+(r-l)/3;
            int rmid=r-(r-l)/3;
            if(check(lmid)>check(rmid))
                l=lmid;
            else r=rmid;
        }
        if(check((l+r)>>1)>check(l)) l=(l+r)>>1;
        printf("%d\n",check(l));
    }
    return 0;
}