Problem:
Score : 400 points

Problem Statement

You are given N integers; the i-th of them is A_i.
Find the maximum possible sum of the absolute differences between the adjacent elements after arranging these integers in a row in any order you like.

Constraints

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the maximum possible sum of the absolute differences between the adjacent elements after arranging the given integers in a row in any order you like.

Sample Input 1

5
6
8
1
2
3

Sample Output 1

21

When the integers are arranged as 3,8,1,6,2, the sum of the absolute differences between the adjacent elements is |3 - 8| + |8 - 1| + |1 - 6| + |6 - 2| = 21. This is the maximum possible sum.

Sample Input 2

6
3
1
4
1
5
9

Sample Output 2

25

Sample Input 3

3
5
5
1

Sample Output 3

8

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>

int compare(const void *a, const void *b){
	long long int *A = (long long int *)a;
	long long int *B = (long long int *)b;
	if (*A > *B) return 1;
	if (*A < *B) return -1;
	return 0;
}

long long ab(long long x){
	if(x<0)return -x;
	return x;
}

int main(){
	int N,i;
	scanf("%d",&N);
	long long A[N],B[N],C[N];
	long long ans=0,tmp=0;
	for(i=0;i<N;i++)scanf("%lld",&A[i]);
	qsort(A,N,sizeof(long long),compare);
	B[N/2]=A[0];
	int min=1;
	int max=N-1;
	for(i=1;i<=(N+1)/2-1;i++){
		if(i%2==1){
			B[N/2-i]=A[max--];
			B[N/2+i]=A[max--];
		}else{
			B[N/2-i]=A[min++];
			B[N/2+i]=A[min++];
		}
	}
	if(N%2==0)B[0]=A[N/2];
	for(i=0;i<N-1;i++)ans+=ab(B[i]-B[i+1]);
	
	C[N/2]=A[N-1];
	min=0;
	max=N-2;
	for(i=1;i<=(N+1)/2-1;i++){
		if(i%2==1){
			C[N/2-i]=A[min++];
			C[N/2+i]=A[min++];
		}else{
			C[N/2-i]=A[max--];
			C[N/2+i]=A[max--];
		}
	}
	if(N%2==0)C[0]=A[N/2];
	for(i=0;i<N-1;i++)tmp+=ab(C[i]-C[i+1]);
	if(tmp>ans)ans=tmp;
	
	printf("%lld\n",ans);
	return 0;
}