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,*a=map(int,open(0).read().split())
if n<3:
    print(abs(a[0]-a[1]))
    exit()
b=sorted(a)
c=abs(b[0]-b[-1])+abs(b[0]-b[-2])
x,y=b[-1],b[-2]
del b[-1],b[-1],b[0]
while b:
    if len(b)<2:
        c+=max(abs(x-b[0]),abs(y-b[0]))
        del b[0]
    else:
        if min(x,y)>b[-1]:
            c+=max(abs(x-b[0])+abs(y-b[1]),abs(x-b[1])+abs(y-b[0]))
            x,y=b[0],b[1]
            del b[0],b[0]
        else:
            c+=max(abs(x-b[-1])+abs(y-b[-2]),abs(x-b[-2])+abs(y-b[-1]))
            x,y=b[-1],b[-2]
            del b[-1],b[-1]
print(c)