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

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long LL;
const int maxn=1e5+10;
int n;
int a[maxn],b[maxn];

int main() {
    scanf("%d",&n);
    for (int i=1;i<=n;i++) scanf("%d",&a[i]);
    sort(a+1,a+1+n);
    LL sum=abs(a[1]-a[n])+abs(a[1]-a[n-1]);
    b[n]=b[n-1]=1;
    int ed=n;
    for (int i=2;i<=ed;i++) {
        int tmp=ed-i+1;
        if (tmp<3) break;
        if (tmp==3) {
            sum+=abs(a[i]-a[ed]);
            break;
        }
        else if (tmp==4) {
            sum+=abs(a[i]-a[ed])+abs(a[i+1]-a[ed-1]);
            break;
        }
        int cnt=0;
        for (int j=ed;j>i;j--) {
            if (cnt==0 && b[j]<2) {
                cnt++;
                sum+=abs(a[i]-a[j]);
                b[j]++;
                if (b[j]==2) ed=j-1;
            } else if (cnt==1 && b[j]<1) {
                cnt++;
                sum+=abs(a[i]-a[j]);
                b[j]++;
            }
            if (cnt==2) break;
        }
    }
    printf("%lld\n", sum);
    return 0;
}