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 Rust (1.42.0) (judge verdict: Accepted)

use itertools::Itertools;

fn main() {
    proconio::input!(n: usize, a: [i64; n]);
    let a = a.into_iter().sorted().collect_vec();
    let ans: i64 = if n % 2 == 0 {
        let m = std::iter::repeat(-2)
            .take(n / 2 - 1)
            .chain(std::iter::once(-1))
            .chain(std::iter::once(1))
            .chain(std::iter::repeat(2).take(n / 2 - 1));
        a.iter().zip(m).map(|(a, m)| a * m).sum()
    } else {
        let m1 = std::iter::repeat(-2)
            .take(n / 2)
            .chain(std::iter::repeat(1).take(2))
            .chain(std::iter::repeat(2).take(n / 2 - 1));
        let m2 = std::iter::repeat(-2)
            .take(n / 2 - 1)
            .chain(std::iter::repeat(-1).take(2))
            .chain(std::iter::repeat(2).take(n / 2));
        std::cmp::max(
            a.iter().zip(m1).map(|(a, m)| a * m).sum(),
            a.iter().zip(m2).map(|(a, m)| a * m).sum(),
        )
    };
    println!("{}", ans);
}