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)

#[allow(unused_imports)]
use itertools::Itertools;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn main() {
    input! {
        n: usize,
        a: [i64; n],
    }

    let mut a = a
        .into_iter()
        .sorted()
        .collect::<std::collections::VecDeque<_>>();

    let mut l = a.pop_front().unwrap();
    let mut r = l;
    let mut res = 0;
    while let (Some(f), Some(b)) = (a.front(), a.back()) {
        let x = *[
            ((f - l).abs(), 0),
            ((f - r).abs(), 1),
            ((b - l).abs(), 2),
            ((b - r).abs(), 3),
        ]
        .iter()
        .max()
        .unwrap();
        res += x.0;
        if x.1 == 0 {
            l = *f;
            a.pop_front();
        } else if x.1 == 1 {
            r = *f;
            a.pop_front();
        } else if x.1 == 2 {
            l = *b;
            a.pop_back();
        } else if x.1 == 3 {
            r = *b;
            a.pop_back();
        }
    }
    println!("{}", res);
}