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())
arr=[int(input()) for _ in range(n)]
arr=sorted(arr)
ans=0
l=1
r=n-3
lnum=arr[-1]
rnum=arr[-2]
if n==2:
  print(abs(arr[0]-arr[1]))
else:
  ans=(arr[-1]-arr[0])+(arr[-2]-arr[0])
  while 1:
    if r-l==-1:
      break
    if arr[r]-min(lnum,rnum)>=max(lnum,rnum)-arr[l]:
      if lnum==min(lnum,rnum):
        ans+=arr[r]-lnum
        lnum=arr[r]
        r-=1
      else:
        ans+=arr[r]-rnum
        rnum=arr[r]
        r-=1
    else:
      if lnum==max(lnum,rnum):
        ans+=lnum-arr[l]
        lnum=arr[l]
        l+=1
      else:
        ans+=rnum-arr[l]
        rnum=arr[l]
        l+=1
  print(ans)