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()
ans = 0
if N%2==0:
    B1 = A[:N//2]
    B2 = A[N//2:]
    ans = 2*(sum(B2)-sum(B1)) + B1[-1] - B2[0]
else:
    B1 = A[:N//2]
    B2 = A[N//2:]
    p = 2*(sum(B2)-sum(B1)) - B2[0] - B2[1]

    C1 = A[:N//2+1]
    C2 = A[N//2+1:]
    q = 2*(sum(C2)-sum(C1)) + C1[-1] + C1[-2]
    ans = max(p, q)

print(ans)