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 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define _GLIBCXX_DEBUG
using namespace std;
using ll = long long;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep2(i, s, n) for (int i = (s); i < (int)(n); i++)
int main() {
  int64_t N;
  cin >> N;
  vector<int64_t> vec(N);
  vector<int64_t> vecR(N);
  int64_t sum = 0;
  rep(i, N) {
    cin >> vec.at(i);
    vecR.at(i) = vec.at(i);
    sum += vec.at(i);
  }
  sort(vec.begin(), vec.end());
  sort(vecR.begin(), vecR.end());
  reverse(vecR.begin(), vecR.end());
  int64_t A, B, C, D;
  A = B = C = D = 0;
  int64_t X, Y;
  X = Y = 0;
  if(N % 2 == 0) {
    rep(i, N/2) {
      A += vec.at(i);
      B += vecR.at(i);
    }
    cout << B * 2 - A * 2 - vec.at(N/2) + vecR.at(N/2) << endl;
  }
  else {
    rep(i, N/2) {
      A += vecR.at(i+N/2); 
      B += vecR.at(i);
    }
    rep2(i, N/2, N/2+2) {
      X += vec.at(i);
      Y += vecR.at(i);
    }
    rep(i, N/2) {
      C += vec.at(i+N/2);  
      D += vec.at(i);       
    }
    cout << max(B * 2 - (sum - B) * 2 + Y, (sum - D) * 2 - X - 2 * D) << endl;
  }
}