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 (3.8.2) (judge verdict: Wrong Answer)

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

l.sort()


if n%2==0:
  a=l[:n//2]
  b=l[n//2:]
  a=a[::-1]
  b=b[::-1]


  ans=0
  mae=a[0]
  for i in range(len(a)):
    ans+=abs(a[i]-b[i])
    ans+=abs(a[i]-mae)
    mae=b[i]
  print(ans)
else:
  a=l[:n//2]
  b=l[n//2:]
  a=a[::-1]
  b=b[::-1]

  ans1=0
  ans2=0

  for i in range(len(a)):
    ans1+=abs(a[i]-b[i])+abs(a[i]-b[i+1])

  a=l[:n//2+1]
  b=l[n//2+1:]
  a=a[::-1]
  b=b[::-1]

  for i in range(len(b)):
    ans2+=abs(b[i]-a[i])+abs(b[i]-a[len(a)-i-1])

  print(max(ans1,ans2))