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)

n = int(input())
a = [int(input()) for _ in range(n)]
a.sort(reverse=True)

ans = 0
if n % 2 == 0:
    plus = a[:n//2]
    minus = a[n//2:]
    ans = (2*sum(plus)-plus[-1]) - (2*sum(minus)-minus[0])
else:
    ans1 = 0
    plus = a[:n//2]
    minus = a[n//2:]
    ans1 = (2*sum(plus)) - (2*sum(minus)-minus[0]-minus[1])

    ans2 = 0
    plus = a[:(n+1)//2]
    minus = a[(n+1)//2:]
    minus.sort()
    ans2 = (2*sum(plus)-plus[-1]-plus[-2]) - (2*sum(minus))

    ans = max(ans1, ans2)

print(ans)