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(non_snake_case, unused)]
use std::cmp::*;
use std::collections::*;

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($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)*}
    };
}

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)*}
    };
}

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, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (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")
    };
}

fn main() {
    input! {
        n: usize,
        mut a: [i64; n],
    }
    a.sort();
    let mut a_ = VecDeque::new();
    for i in 0..n {
        a_.push_back(a[i]);
    }
    let mut ans = 0i64;
    let mut posi = 0i64;
    let mut nega = 0i64;
    //left
    for i in 0..n - 2 {
        if i % 2 == 0 {
            let v = a_.pop_front().unwrap();
            nega += v * 2;
        } else {
            let v = a_.pop_back().unwrap();
            posi += v * 2;
        }
    }
    if n % 2 == 1 {
        for i in 0..2 {
            let v = a_.pop_back().unwrap();
            posi += v;
        }
    } else {
        let v = a_.pop_front().unwrap();
        nega += v;
        let v = a_.pop_back().unwrap();
        posi += v;
    }
    ans = max(ans, posi - nega);

    //right
    posi = 0;
    nega = 0;
    a.reverse();
    let mut a_ = VecDeque::new();
    for i in 0..n {
        a_.push_back(a[i]);
    }
    for i in 0..n - 2 {
        if i % 2 == 0 {
            let v = a_.pop_front().unwrap();
            nega += v * 2;
        } else {
            let v = a_.pop_back().unwrap();
            posi += v * 2;
        }
    }
    if n % 2 == 1 {
        for i in 0..2 {
            let v = a_.pop_back().unwrap();
            posi += v;
        }
    } else {
        let v = a_.pop_front().unwrap();
        nega += v;
        let v = a_.pop_back().unwrap();
        posi += v;
    }

    ans = max(ans, nega - posi);

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