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: Accepted)

import copy
N = int(input())
A = [int(input()) for _ in range(N)]
A.sort()
B = copy.deepcopy(A)
sum1 = 0
sum2 = 0
center = -(-N // 2) - 1
if N%2 == 1:
    for i in range(N):
        if i == 0:
            beforeNum = A.pop(center)
        else:
            if i%2 == 1:
                num = A.pop(-1)
            else:
                num = A.pop(0)
            sum1 += abs(beforeNum - num)
            beforeNum = num
    for i in range(N):
        if i == 0:
            beforeNum = B.pop(center)
        else:
            if i%2 == 1:
                num = B.pop(0)
            else:
                num = B.pop(-1)
            sum2 += abs(beforeNum - num)
            beforeNum = num
else:
    for i in range(N):
        if i == 0:
            beforeNum = A.pop(center)
        else:
            if i%2 == 1:
                num = A.pop(-1)
            else:
                num = A.pop(0)
            sum1 += abs(beforeNum - num)
            beforeNum = num
    center = center + 1
    for i in range(N):
        if i == 0:
            beforeNum = B.pop(center)
        else:
            if i%2 == 1:
                num = B.pop(0)
            else:
                num = B.pop(-1)
            sum2 += abs(beforeNum - num)
            beforeNum = num
print(max(sum1,sum2))