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: Accepted)

from collections import*
n,*a=map(int,open(0).read().split())
def f(a):
  a=deque(a)
  deq=deque([a.popleft()])
  for i in range(n-1):
    if i%4==0:
      deq.appendleft(a.pop())
    elif i%4==1:
      deq.append(a.pop())
    elif i%4==2:
      deq.appendleft(a.popleft())
    else:
      deq.append(a.popleft())
  l=list(deq)
  return sum(abs(i-j)for i,j in zip(l,l[1:]))
s=sorted(a)
print(max(f(s),f(s[::-1])))