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 = sorted([int(input()) for _ in range(n)])

l = a[0]
r = a[0]
ixl = 1
ixr = n-1

s = 0
d = -1

while ixl < ixr:
    if d == 1:
        nl = a[ixl]
        nr = a[ixl+1]
        ixl += 2
    else:
        nl = a[ixr]
        nr = a[ixr-1]
        ixr -= 2
    s += ((l+r)-(nl+nr))*d
    l = nl
    r = nr
    d *= -1
if ixl == ixr:
    s += (l-a[ixl])*d
s1 = s

a.reverse()

l = a[0]
r = a[0]
ixl = 1
ixr = n-1

s = 0
d = 1

while ixl < ixr:
    if d == -1:
        nl = a[ixl]
        nr = a[ixl+1]
        ixl += 2
    else:
        nl = a[ixr]
        nr = a[ixr-1]
        ixr -= 2
    s += ((l+r)-(nl+nr))*d
    l = nl
    r = nr
    d *= -1
if ixl == ixr:
    s += (l-a[ixl])*d
s = max(s, s1)

print(s)