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)

N = int(input())
A = [int(input()) for _ in range(N)]
A.sort()

s = int((N - 1) / 2)
m = A[0:s+1]
M = A[s+1:][::-1]

ans = [0 for _ in range(N)]

li = s
ri = s + 1

for i, (a, b) in enumerate(zip(m, M)):
    if i % 2 == 1:
        a, b = b, a
    ans[li] = a
    ans[ri] = b
    li -= 1
    ri += 1

if N % 2 == 1:
    ans[0] = m[-1]

S = 0
for i, j in zip(ans[1:], ans[:-1]):
    S += abs(i - j)

print(S)