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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<stdio.h>
#include<stdlib.h>
#define inf 5000000000000000

int sortfncsj(const void *a,const void *b){
    if(*(int*)a == *(int*)b){return 0;}
    if(*(int*)a < *(int*)b){return -1;}
    return 1;
}

int sortfnckj(const void *a,const void *b){
    if(*(int*)a == *(int*)b){return 0;}
    if(*(int*)a > *(int*)b){return -1;}
    return 1;
}

long long max(long long a,long long b){
	if(a < b){return b;}return a;
}

int main(void){
	long long n,fa[131072],ma[131072],la[131072],i;
	long long fasm[131072],mfsm[131072],mlsm[131072],lasm[131072];
	long long msc = -inf,j,k,x;
	long long fc[131072],lc[131072];
	long long fcz[131072],lcz[131072];
	scanf("%lld",&n);
	for(i = 0;i < 3*n;i++){scanf("%lld",&fa[i]);}
	for(i = 0;i <= n;i++){
		for(j = 0;j <= n;j++){
			for(k = 0;k < n+j;k++){
				fc[k]=fa[k];
			}
qsort(fc,n+j,sizeof(long long),sortfnckj);
			for(k = 0;k < n+(n-j);k++){
				lc[k] = fa[(n+j+k)];
			}
qsort(lc,n+(n-j),sizeof(long long),sortfncsj);
		x=0;for(i = 0;i < n;i++){x=x+fc[i]-lc[i];}
		}
		msc=max(msc,x);
	}
	printf("%lld\n",msc);
	return 0;
}