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)

N = int(input())

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

def factorial(n):
   if n == 0: return 1
   return n * factorial(n-1)

def array_patterns(origin):
    patterns = []
    for i in range(factorial(len(origin))):
        _origin = []
        for j in range(len(origin)):
            _origin.append(origin[j])
        patterns.append(_origin)
    return patterns

diff = []
for _A in list(array_patterns(A)):
    _diff = 0
    for i in range(N - 1):
        _diff += abs(_A[i] - _A[i + 1])
    diff.append(int(_diff))

print(max(diff))