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: Accepted)

def calc_score(li):
    prev = li[0]
    ret = 0
    for el in li:
        ret += abs(el - prev)
        prev = el
    return ret


N, *A = map(int, open(0).read().split())
A = sorted(A)
if N % 2:
    ans = 0
    li = [0] * N
    li[0] = A[N // 2]
    for i in range(N // 2):
        li[i * 2 + 1] = A[i + N // 2 + 1]
        li[i * 2 + 2] = A[i]
    ans = calc_score(li)
    li[N - 1] = A[N // 2]
    for i in range(N // 2):
        li[i * 2] = A[i + N // 2 + 1]
        li[i * 2 + 1] = A[i]
    print(max(ans, calc_score(li)))
else:
    li = [0] * N
    for i in range(N // 2):
        li[i * 2] = A[i + N // 2]
        li[i * 2 + 1] = A[i]
    print(calc_score(li))