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)

from collections import deque
N = int(input())
A = []
for i in range(N):
    a = int(input())
    A.append(a)

A = sorted(A)
q = deque()
q.append(A[0])
i = 1
j = N - 1
mi = True
while i < N and j > 0 and i <= j:
    if mi:
        p1, p2 = q[0], q[-1]
        if abs(A[j] - p1) < abs(A[j] - p2):
            q.append(A[j])
        else:
            q.appendleft(A[j])
        j -= 1
        mi = False
    else:
        p1, p2 = q[0], q[-1]
        if abs(A[i] - p1) < abs(A[i] - p2):
            q.append(A[i])
        else:
            q.appendleft(A[i])
        i += 1
        mi = True

num = 0
pre = q[0]
for i in range(1, N):
    num += abs(q[i] - pre)
    pre = q[i]

print(num)