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())

a=[]

for i in range(n):
    b=int(input())
    a.append(b)
    
a.sort()

ans=["" for i in range(n)]

ans[n//2]=a[-1]
a.remove(a[-1])
l=(n//2)-1
r=(n//2)+1

for i in range(n-1):
    if i%4==0:
        ans[l]=a[0]
        a.remove(a[0])
        l-=1
    elif i%4==1:
        ans[r]=a[0]
        a.remove(a[0])
        r+=1
    elif i%4==2:
        ans[l]=a[-1]
        a.remove(a[-1])
        l-=1
    elif i%4==3:
        ans[r]=a[-1]
        a.remove(a[-1])
        r-=1

ans.append(ans[0])     
num=0
num2=0
num3=0


for i in range(n):
    num+=abs(ans[i]-ans[i+1])

num-=min(abs(ans[0]-ans[1]),abs(ans[-1]-ans[-2]),abs(ans[-2]-ans[-3]))
        
print(num)