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 PyPy3 (2.4.0) (judge verdict: Accepted)

n,*a=map(int,open(0).readlines())
a.sort()
if n%2:
  b=a[:n//2]
  c=a[n//2:]
  for i in range(n//2):
    b[i]*=2
  for i in range(2,n//2+1):
    c[i]*=2
  m=sum(c)-sum(b)
  b=a[:n//2+1]
  c=a[n//2+1:]
  for i in range(n//2-1):
    b[i]*=2
  for i in range(n//2):
    c[i]*=2
  m=max(m,sum(c)-sum(b))
else:
  b=a[:n//2]
  c=a[n//2:]
  for i in range(n//2-1):
    b[i]*=2
  for i in range(1,n//2):
    c[i]*=2
  m=sum(c)-sum(b)
print(m)