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)

from collections import deque
n = int(input())
A = []
for _ in range(n):
    A.append(int(input()))
dq = deque(sorted(A))
ans = deque([dq.popleft()])
ans.append(dq.pop())
ans.appendleft(dq.pop())
flag = True
while dq:
    if flag:
        ans.append(dq.popleft())
        if dq:
            ans.appendleft(dq.popleft())
            flag = False
    else:
        ans.append(dq.pop())
        if dq:
            ans.appendleft(dq.pop())
            flag = True
B = list(ans)
s = 0
for i in range(n-1):
    s += abs(B[i+1]-B[i])
print(s)