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::collections::VecDeque;

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 main() {
    let n: usize = read();
    let mut v: Vec<i64> = Vec::new();
    for _ in 0..n {
        v.push(read());
    }
    v.sort();
    let mut ascend_order: VecDeque<_> = v.iter().collect();
    let mut descend_order: VecDeque<_> = v.iter().rev().collect();

    let mut array_result = std::collections::VecDeque::new();

    let mut cnt = 0;
    array_result.push_back(ascend_order.pop_front().unwrap());
    // println!("a {:?}", ascend_order);
    // println!("d {:?}", descend_order);

    loop {
        if cnt % 2 == 1 {
            array_result.push_front(ascend_order.pop_front().unwrap());
            if array_result.len() == n {
                break;
            }
            array_result.push_back(ascend_order.pop_front().unwrap());
            if array_result.len() == n {
                break;
            }
        } else {
            array_result.push_front(descend_order.pop_front().unwrap());
            if array_result.len() == n {
                break;
            }
            array_result.push_back(descend_order.pop_front().unwrap());
            if array_result.len() == n {
                break;
            }
        }
        cnt += 1
    }
    // println!("{:?}", array_result);

    let mut ans: i64 = 0;
    let mut past = array_result.pop_front().unwrap();
    while !array_result.is_empty() {
        let cur = array_result.pop_front().unwrap();
        ans += (cur - past).abs();
        past = cur;
    }
    // println!("{:?}", ans);

    let mut ascend_order: VecDeque<_> = v.iter().collect();
    let mut descend_order: VecDeque<_> = v.iter().rev().collect();

    let mut array_result = std::collections::VecDeque::new();

    let mut cnt = 0;
    array_result.push_back(descend_order.pop_front().unwrap());
    // println!("a {:?}", ascend_order);
    // println!("d {:?}", descend_order);

    loop {
        if cnt % 2 == 0 {
            array_result.push_front(ascend_order.pop_front().unwrap());
            if array_result.len() == n {
                break;
            }
            array_result.push_back(ascend_order.pop_front().unwrap());
            if array_result.len() == n {
                break;
            }
        } else {
            array_result.push_front(descend_order.pop_front().unwrap());
            if array_result.len() == n {
                break;
            }
            array_result.push_back(descend_order.pop_front().unwrap());
            if array_result.len() == n {
                break;
            }
        }
        cnt += 1
    }
    // println!("{:?}", array_result);

    let mut ans2: i64 = 0;
    let mut past = array_result.pop_front().unwrap();
    while !array_result.is_empty() {
        let cur = array_result.pop_front().unwrap();
        ans2 += (cur - past).abs();
        past = cur;
    }
    println!("{:?}", std::cmp::max(ans, ans2));
}