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())
A = []
for i in range(n):
    A.append(int(input()))
    
A.sort()
B = []
left = 0
right = 0
res = 0
for i in range(n):
    if(i==0):
        tmp = A.pop(0)
        left = tmp
        right = tmp
    elif(i==n-1):
        if(i%2==0):
            tmp = A.pop()
            res += abs(left-tmp)
        else:
            tmp = A.pop()
            if(abs(right-tmp)>abs(left-tmp)):
                res += abs(right-tmp)
            else:
                res += abs(left-tmp)
    elif(not(i%4==0 or (i+1)%4==0)):
        if(i%2==1):
            tmp = A.pop()
            res += abs(right-tmp)
            right = tmp
        else:
            tmp = A.pop()
            res += abs(left-tmp)
            left = tmp
    else:
        if(i%2==1):
            tmp = A.pop(0)
            res += abs(right-tmp)
            right = tmp
        else:
            tmp = A.pop(0)
            res += abs(left-tmp)
            left = tmp

print(res)