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 (3.4.3) (judge verdict: Accepted)

from collections import deque

def main():
    N = int(input())
    A = deque(sorted((int(input()) for i in range(N))))
    dq = deque()
    dq.append(A.popleft())
    ans = 0
    for _ in range(N-1):
        a_first = A[0]
        a_last = A[-1]
        dq_first = dq[0]
        dq_last = dq[-1]

        ff = abs(a_first-dq_first)
        fl = abs(a_first-dq_last)
        lf = abs(a_last-dq_first)
        ll = abs(a_last-dq_last)

        comp_list = [ff, fl, lf, ll]
        max_idx = comp_list.index(max(comp_list))
        if max_idx == 0:
            ans += ff
            dq.appendleft(A.popleft())
        elif max_idx == 1:
            ans += fl
            dq.append(A.popleft())
        elif max_idx == 2:
            ans += lf
            dq.appendleft(A.pop())
        else:
            ans += ll
            dq.append(A.pop())

    print(ans)
if __name__ == "__main__":
    main()