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.

5
6
8
1
2
3

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.

6
3
1
4
1
5
9

25

3
5
5
1

8