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 (7.3.0) (judge verdict: Accepted)

from collections import deque
n=int(input())
a=deque(sorted([int(input()) for _ in range(n)]))
b=deque([a.pop()])
i=0
while a:
  if max(abs(a[-1]-b[-1]),abs(a[-1]-b[0]),abs(a[0]-b[-1]),abs(a[0]-b[0]))==abs(a[-1]-b[-1]):
    b.append(a.pop())
  elif max(abs(a[-1]-b[-1]),abs(a[-1]-b[0]),abs(a[0]-b[-1]),abs(a[0]-b[0]))==abs(a[-1]-b[0]):
    b.appendleft(a.pop())
  elif max(abs(a[-1]-b[-1]),abs(a[-1]-b[0]),abs(a[0]-b[-1]),abs(a[0]-b[0]))==abs(a[0]-b[0]):
    b.appendleft(a.popleft())
  else:
    b.append(a.popleft())
ans=0
for i in range(n-1):
  ans+=abs(b[i]-b[i+1])
print(ans)