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 = list(0 for i in range(n))
b = list(0 for i in range(n))

if n%2==0:
    cent  = int(n/2)
else:
    cent = int((n-1)/2)

for i in range(n):
    a[i] = int(input())
a.sort()

for i in range(n):
    if i==0:
        b[cent] = a[i]
    elif i%4==1:
        if i == n-1:
            b[0] = a[n-1-int(i/2)]
        else:
            b[cent-int((i+1)/2)] = a[n-1-int(i/2)]
            b[cent+int((i+1)/2)] = a[n-1-int((i+1)/2)]
    elif i%4==3:
        if i == n-1:
            b[0] = a[int(i/2)]
        else:
            b[cent-int((i+1)/2)] = a[int(i/2)]
            b[cent+int((i+1)/2)] = a[int((i+1)/2)]    

sum = 0
for i in range(1,n):
    sum += abs(b[i]-b[i-1])
print(sum)