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)

n = int(input())
a = [int(input()) for _ in range(n)]
la = len(a)
a.sort()

l = a[0]
r = a[0]
ans = 0
for i in range(la//2):
    if (la-1) % 2 == 1 and i == la//2-1:
        x = a[i+1]
        ans += max(abs(l-x), abs(r-x))
        break

    if i % 2 == 0:
        x = a[la-i-1]
        y = a[la-i-2]
        ans += max(abs(l-x)+abs(r-y), abs(l-y)+abs(r-x))
    else:
        x = a[i]
        y = a[i+1]
        ans += max(abs(l-x)+abs(r-y), abs(l-y)+abs(r-x))
    l = x
    r = y

print(ans)