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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <cmath>
#include <algorithm>
#include <vector>
using namespace std;

pair<int, int> p1[200001], p2[200001];

int main() {
    int n;
    cin >> n;
    vector<int> a;
    long long ans = 0;
    int l = 0, r = 0;
    int ll = 0, rr = n - 2;
    for (int i = 0; i < n; i++) {
        cin >> l;
        a.push_back(l);
    }
    sort(a.begin(), a.end());
    l = a[n - 1];
    r = a[n - 1];
    while (rr - ll >= 0) {
        int mx = 0;
        mx = max(mx, abs(l - a[ll]));
        mx = max(mx, abs(l - a[rr]));
        mx = max(mx, abs(r - a[ll]));
        mx = max(mx, abs(r - a[rr]));
        if (mx == abs(l - a[ll])) {
            l = a[ll];
            ll++;
        } else if (mx == abs(l - a[rr])) {
            l = a[rr];
            rr--;
        } else if (mx == abs(r - a[ll])) {
            r = a[ll];
            ll++;
        } else if (mx == abs(r - a[rr])) {
            r = a[rr];
            rr--;
        }
        ans += mx;
    }
    cout << ans;
    return 0;
}