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: Wrong Answer)

from collections import deque

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

a.sort()
deq = deque(a)

ans = 0

left, right = deq.popleft(), 0
cnt = 1


def comparison(left, right, x, y):
    if y == 0:
        return max(abs(left - x), abs(right - x))

    if right == 0:
        return abs(left*2 - x - y)
    else:
        return abs(left+right-x-y)


while deq:
    if len(deq) == 1:
        x = deq.pop()
        y = 0
    else:
        if cnt:
            x = deq.pop()
            y = deq.pop()
        else:
            x = deq.popleft()
            y = deq.popleft()

    ans += comparison(left, right, x, y)
    left, right = x, y
    cnt = 1-cnt

print(ans)