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: Runtime Error)

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>

#include <algorithm>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>

#include <cassert>
#include <functional>

typedef long long ll;
using namespace std;

#define debug(x) cerr << #x << " = " << x << endl;


#define mod 1000000007 //1e9+7(prime number)
#define INF 1000000000 //1e9
#define LLINF 2000000000000000000LL //2e18
#define SIZE 10000


int main() {
  int N, A[SIZE], B[SIZE];
  ll ans = 0;

  cin >> N;

  for (int i = 0; i < N; i++) {
    cin >> A[i];
  }

  sort(A, A + N);

  for (int _ = 0; _ < 2; _++) {
    for (int i = 0; i < N / 2; i++) {
      B[i * 2 + 1] = A[i];
    }

    for (int i = 0; i < N - N / 2; i++) {
      B[i * 2] = A[i + N / 2];
    }

    ll sum = 0;

    for (int i = 0; i < N - 1; i++) {
      sum += abs(B[i] - B[i + 1]);
    }

    ans = max(ans, sum);
    reverse(A, A + N);
  }

  cout << ans << endl;


  return 0;
}