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)

def cul(low, high):
    high = high[::-1]
    lists = []
    if len(low) > len(high):
        low.insert(0, low[-1])
        low = low[:-1]
        lists.append(low[0])
        for _l, _h in zip(low[1:], high):
            lists.append(_h)
            lists.append(_l)
    elif len(low) < len(high):
        high.insert(0, high[-1])
        high = high[:-1]
        lists.append(high[0])
        for _l, _h in zip(low, high[1:]):
            lists.append(_l)
            lists.append(_h)
    else:
        for _l, _h in zip(low, high):
            lists.append(_l)
            lists.append(_h)
    print(lists)
    ans = 0
    for _p, _n in zip(lists, lists[1:]):
        ans += abs(_n - _p)
    return ans


n = int(input())
a = sorted([int(input()) for _ in range(n)])
if len(a) % 2 == 1:
    lower = a[:len(a) // 2 + 1]
    higher = a[len(a) // 2 + 1:]
    first = cul(lower, higher)
    lower = a[:len(a) // 2]
    higher = a[len(a) // 2:]
    second = cul(lower, higher)
    print(max(first, second))
else:
    lower = a[:len(a) // 2]
    higher = a[len(a) // 2:]
    print(cul(lower, higher))