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: Accepted)

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


fn main() {
    let n = read_one::<usize>();
    let mut an = Vec::new();
    for _ in 0..n {
        an.push(read_one::<isize>());
    }

    an.sort();

    let a = diff(an.clone());
    an.reverse();
    let b = diff(an.clone());
    println!("{}", cmp::max(a, b));
}


fn diff(mut an: Vec<isize>) -> usize {

    let mut n = an.len();
    let mut vd = VecDeque::new();
    vd.push_front(an[0]);
    an.remove(0);
    n -= 1;
    for i in 0..n {
        match i % 4 {
            0 => {
                vd.push_back(an[n - i / 2 - 1]);
            },
            1 => {
                vd.push_front(an[n - i / 2 - 2]);
            },
            2 => {
                vd.push_back(an[i / 2 - 1]);
            },
            3 => {
                vd.push_front(an[i / 2]);
            },
            _ => unreachable!(),
        }
    }
    let mut ans = 0;
    for i in 0..n {
        ans += (vd[i] - vd[i + 1]).abs();
    }

    ans as usize
}


#[allow(dead_code)]
fn read<T>() -> Vec<T>
where T:
    std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.split_whitespace()
        .map(|s| s.trim().parse().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_one<T>() -> T
where T:
    std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().parse().unwrap()
}