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 Python (3.8.2) (judge verdict: Wrong Answer)

n = int(input())
a = sorted([int(input()) for _ in range(n)])

if n == 2:
    print(a[1] - a[0])
elif n == 3:
    print(a[2] + a[1] - 2 * a[0])
elif n % 2 == 0:
    ans = 2 * (sum(a[n // 2:]) - sum(a[:n // 2]))
    print(ans + a[n // 2 - 1] - a[n // 2])
elif n % 2 == 1:
    ans = 2 * (sum(a[n // 2 + 1:]) - sum(a[:n // 2 + 1]))
    print(ans + a[n // 2] + a[n // 2 - 1])