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)

/// Thank you tanakh!!!
/// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

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

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

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

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

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

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

use std::cmp;

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

    let mut a = a;
    a.sort();

    if n % 2 == 1 {
        let min_num = (n - 1) / 2;
        let mut minus = 0;
        for i in 0..min_num {
            minus += a[i] * 2;
        }
        let mut plus = a[min_num] + a[min_num + 1];
        for i in (min_num + 2)..n {
            plus += a[i] * 2;
        }
        assert!(plus >= minus);
        let ans1 = plus - minus;

        a.reverse();
        let mut plus = 0;
        for i in 0..min_num {
            plus += a[i] * 2;
        }
        let mut minus = a[min_num] + a[min_num + 1];
        for i in (min_num + 2)..n {
            minus += a[i] * 2;
        }
        assert!(plus >= minus);
        let ans2 = plus - minus;
        println!("{}", cmp::max(ans1, ans2));
    } else {
        let mut plus = 0;
        let mut minus = 0;
        for i in 0..(n / 2) {
            minus += a[i] * 2;
        }
        minus -= a[(n / 2) - 1];

        for i in (n / 2)..n {
            plus += a[i] * 2;
        }
        plus -= a[n / 2];
        println!("{}", plus - minus);
    }
}