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: Time Limit Exceeded)

N=int(input())
A=[int(input()) for x in range(N)]

A.sort()

def solve(a,n):
  cnt=a[0]
    
  c,d=a[-1],a[-2]
  ans=abs(cnt-c)+abs(cnt-d)
  cnt=c+d
  
  a=a[1:-2]
  
  ch=1
  while len(a) > 1:
    if ch==-1:
      c,d=a[-1],a[-2]
      ans+=abs(cnt-(c+d))
      cnt=c+d
      ch=1
      a=a[:-2]
    else:
      c,d=a[0],a[1]
      ans+=abs(cnt-(c+d))
      cnt=c+d
      ch=-1
      a=a[2:]
  
  if len(a)==1:
    ans+=max(abs(c-a[0]),abs(d-a[0]))
    
  return ans

ans1=solve(A,N)
A.sort(reverse=True)
ans2=solve(A,N)
print(max(ans1,ans2))