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)

def c_align(N, A):
    from collections import deque
    tmp = sorted(A)

    seq = tmp[:]
    old_check = seq.pop(-1 + N // 2) if N % 2 == 0 else seq.pop(N // 2)
    current_check = -1
    seq = deque(seq)
    ans1 = 0
    turn = 0
    while seq:
        current_check = seq.pop() if turn % 2 == 0 else seq.popleft()
        ans1 += abs(current_check - old_check)
        old_check = current_check
        turn += 1

    seq = tmp[:]
    old_check = seq.pop(1 + N // 2) if N % 2 == 0 else seq.pop(N // 2)
    current_check = -1
    seq = deque(seq)
    ans2 = 0
    turn = 0
    while seq:
        current_check = seq.popleft() if turn % 2 == 0 else seq.pop()
        ans2 += abs(current_check - old_check)
        old_check = current_check
        turn += 1

    ans = max(ans1, ans2)
    return ans

N = int(input())
A = [int(input()) for _ in range(N)]
print(c_align(N, A))