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)

N = int(input())
A = [int(input()) for i in range(N)]

A_ = sorted(A)
A_r = list(reversed(A_))

l = []
for i, (x, y) in enumerate(zip(A_[:N//2], A_r[:N//2])):
    if i % 2 == 0:
        l.append(x)
        l.insert(0, y)
    else:
        l.append(y)
        l.insert(0, x)

if N % 2 != 0:
    m = A_[N//2]
    if abs(l[0] - m) > abs(l[-1] - m):
        l.insert(0, m)
    else:
        l.append(m)

def g(L):
    for i, j in zip(L[:-1], L[1:]):
        yield abs(i - j)

print(sum(g(l)))