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 (1.15.1) (judge verdict: Wrong Answer)

fn get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

fn readln<T>() -> T
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().parse().unwrap()
}

use std::collections::VecDeque;

fn main() {
    let n = readln();

    let mut xs = vec![];
    for _ in 0..n {
        let x: i64 = readln();
        xs.push(x);
    }
    xs.sort();

    let mut q = VecDeque::new();

    for x in xs {
        q.push_back(x);
    }

    let mut r = VecDeque::new();
    let mut f = false;
    let a = q.pop_front().unwrap();
    r.push_front(a);

    loop {
        if f {
            if let Some(x) = q.pop_front() {
                r.push_front(x);
            }
            else {
                break;
            }
            if let Some(x) = q.pop_front() {
                r.push_back(x);
            }
            else {
                break;
            }
        }
        else {
            if let Some(x) = q.pop_back() {
                r.push_front(x);
            }
            else {
                break;
            }
            if let Some(x) = q.pop_back() {
                r.push_back(x);
            }
            else {
                break;
            }
        }
        f = !f;
    }

    let mut prev: i64 = *r.front().unwrap();
    let mut res = 0;
    //println!("--");
    while let Some(x) = r.pop_front() {
        //println!("{:?}", x);
        res += (prev - x).abs();
        prev = x;
    }


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