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_macros)]
macro_rules! input_byline {
    ($($r:tt)* ) => {
        let stdin = std::io::stdin();
        let mut q = std::collections::VecDeque::new();
        let mut next = || {
            if q.is_empty() {
                let mut s = String::new();
                stdin.read_line(&mut s);
                for v in s.split_whitespace() {
                    q.push_back(v.to_string());
                }
            }
            q.pop_front().unwrap()
        };
        input_inner!{next, $($r)*}
    };

}

#[allow(unused_macros)]
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

trait Printable {
    fn p(&self);
}

impl<T: std::fmt::Display> Printable for T {
    fn p(&self) {
        println!("{}", self);
    }
}

impl<T: std::fmt::Display> Printable for [T] {
    fn p(&self) {
        for i in 0..self.len() {
            if i != 0 {
                print!(" ");
            }
            print!("{}", self[i]);
        }
        println!("");
    }
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap};

#[allow(dead_code)]
type Graph = Vec<Vec<usize>>;

fn main() {
    input! {
        n: usize,
        mut a: [usize; n],
    }

    let mut v1 = std::collections::VecDeque::new();
    let mut v2 = std::collections::VecDeque::new();
    let mut v3 = std::collections::VecDeque::new();
    let mut v4 = std::collections::VecDeque::new();

    a.sort();

    for i in 0..n {
        v1.push_back(a[i]);
        v2.push_back(a[i]);
    }

    v3.push_back(v1.pop_front().unwrap());
    v4.push_back(v2.pop_back().unwrap());

    while !v1.is_empty() {
        if (v3.len() / 2) & 1 == 0 {
            if let Some(x) = v1.pop_back() {
                v3.push_front(x);
            }

            if let Some(x) = v1.pop_back() {
                v3.push_back(x);
            }
        } else {
            if let Some(x) = v1.pop_front() {
                v3.push_front(x);
            }

            if let Some(x) = v1.pop_front() {
                v3.push_back(x);
            }
        }
    }

    while !v2.is_empty() {
        if (v4.len() / 2) & 1 == 1 {
            if let Some(x) = v2.pop_back() {
                v4.push_front(x);
            }

            if let Some(x) = v2.pop_back() {
                v4.push_back(x);
            }
        } else {
            if let Some(x) = v2.pop_front() {
                v4.push_front(x);
            }

            if let Some(x) = v2.pop_front() {
                v4.push_back(x);
            }
        }
    }

    let (mut a1, mut a2) = (0, 0);
    for i in 0..v3.len() - 1 {
        a1 += (v3[i] as i64 - v3[i + 1] as i64).abs() as usize;
        a2 += (v4[i] as i64 - v4[i + 1] as i64).abs() as usize;
    }
    println!("{}", max(a1, a2));
}