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: Runtime Error)

N=int(input())
num=[int(input()) for i in range(N)]
num.sort()

if N%2!=0: #kisu
  manaka=int(N/2)
  if abs(num[manaka]-num[0])<abs(num[manaka]-num[N-1]):
    sum=abs(num[manaka]-num[N-1])
    for i in range(int((N-1)/2)):
      sum+=abs(num[N-1-i]-num[i])
      sum+=abs(num[i]-num[N-2-i])
    print(sum)     
  else:
    jun.append(manaka)
    sum=abs(num[manaka]-num[0])
    for i in range(int((N-1)/2)):
      sum+=abs(num[i]-num[N-1-i])
      sum+=abs(num[i+1]-num[N-1-i])
    print(sum)
else:
  manaka=int(N/2)
  sum=abs(num[manaka]-num[0])
  for i in range(manaka-1):
    sum+=abs(num[i]-num[N-1-i])
    sum+=abs(num[i+1]-num[N-1-i])
  print(sum)