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=sorted([int(input()) for i in range(N)])
#A=[i for i in range(50)]
#N=len(A)
value=0
B,C=A[0],A[0]
i=1
z=0

while N-1>z:

    if z%4==0:
        value+=A[-i]-B
        B=A[-i]
    if z%4==1:
        value+=A[-i-1]-C
        C=A[-i-1]
    if z%4==2:
        value+=B-A[i]
        B=A[i]
    if z%4==3:
        value+=C-A[i+1]
        C=A[i+1]
        i+=2
    #print(B,C,i,z)
    z+=1
value1=value
value=0
B,C=A[-1],A[-1]
i=0
z=0
while N-1>z:

    if z%4==0:
        value+=B-A[i]
        B=A[i]

    if z%4==1:
        value+=C-A[i+1]
        C=A[i+1]

    if z%4==2:
        value+=A[-i-2]-B
        B=A[-i-1]
    if z%4==3:
        value+=A[-i-3]-C
        C=A[-i-2]
        i+=2
    #print(B,C,i,z,value)
    z+=1
value2=value
print(max(value1,value2))