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 std::io::Read;
use std::collections::VecDeque;
use std::cmp::max;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let mut a: Vec<isize> = (0..n).map(|_| iterator.next().unwrap().parse().unwrap()).collect();

    a.sort();
    let mut ans: isize = 0;
    for i in 0..4 {
        let mut q: VecDeque<isize> = a.clone().into_iter().collect();
        let mut result: VecDeque<isize> = VecDeque::new();
        let mut count: usize = i;
        while !q.is_empty() {
            match count % 4 {
                0 => {
                    result.push_back(q.pop_front().unwrap());
                },
                1 => {
                    result.push_front(q.pop_back().unwrap());
                },
                2 => {
                    result.push_back(q.pop_back().unwrap());
                },
                _ => {
                    result.push_front(q.pop_front().unwrap());
                },
            }
            count += 1;
        }

        let mut s = 0;
        for i in 1..n {
            s += (result[i] - result[i - 1]).abs();
        }
        ans = max(ans, s);
    }
    ans.to_string()
}