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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let n = read::<usize>();
    let mut a = vec![];
    for _ in 0..n {
        a.push(read::<i64>());
    }
    a.sort();
    let mut ans = 0;
    if n % 2 == 1 {
        let mut lower = vec![];
        let mut upper = vec![];
        for i in 0..(n - n / 2) {
            lower.push(a[i]);
        }
        for i in (n - n / 2)..n {
            upper.push(a[i]);
        }
        let mut ans1 = upper.iter().sum::<i64>() * 2;
        ans1 -= lower.iter().sum::<i64>() * 2;
        ans1 += lower[lower.len() - 1];
        ans1 += lower[lower.len() - 2];

        let mut lower = vec![];
        let mut upper = vec![];
        for i in 0..(n / 2) {
            lower.push(a[i]);
        }
        for i in (n / 2)..n {
            upper.push(a[i]);
        }
        let mut ans2 = upper.iter().sum::<i64>() * 2;
        ans2 -= lower.iter().sum::<i64>() * 2;
        ans2 -= upper[0];
        ans2 -= upper[1];
        ans = max(ans1, ans2);
    } else {
        let mut lower = vec![];
        let mut upper = vec![];
        for i in 0..(n / 2) {
            lower.push(a[i]);
        }
        for i in (n / 2)..n {
            upper.push(a[i]);
        }
        ans = upper.iter().sum::<i64>() * 2;
        ans -= upper[0];
        ans -= lower.iter().sum::<i64>() * 2;
        ans += lower[lower.len() - 1];
    }

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

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}