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())
X = [int(input()) for i in range(N)]
X = sorted(X)

if N%2 == 0:
    n = N//2
    print(sum(X[:n-1])*(-2) + sum(X[n+1:])*2 + X[n] - X[n-1])
else:
    n = (N-1)//2
    print(max(sum(X[:n-1])*(-2) + sum(X[n+1:])*2 - X[n] - X[n-1], sum(X[:n])*(-2) + sum(X[n+2:])*2 + X[n] + X[n+1]))