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: Time Limit Exceeded)

#include<stdio.h>
#include<stdlib.h>
#define max(a,b) (((a)>(b))?(a):(b))
long long a[300000],b[200000],c[200000];
int cmp(const void *x,const void *y){
	return *(long long*)x - *(long long*)y;
}
int main(int argc, char const *argv[]){
	long n,i,j;
	long long ans=-100000000000000,p;
	scanf("%ld",&n);
	for(i=0;i<n*3;i++){
		scanf("%ld",&a[i]);
	}
	for(i=0;i<=n;i++){
		for(j=0;j<n+i;j++){
			b[j]=a[j];
		}
		for(j=n+i;j<3*n;j++){
			c[j-n-i]=a[j];
		}
		qsort(b,n+i,sizeof(long long),cmp);
		qsort(c,2*n-i,sizeof(long long),cmp);
		p=0;
		for(j=0;j<n;j++){
			p+=b[n+i-1-j];
		}
		for(j=0;j<n;j++){
			p-=c[j];
		}
		ans=max(ans,p);
	}
	printf("%lld\n",ans);
	return 0;
}