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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

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

    aa.sort();

    let ans = if n % 2 == 0 {
        let mid = n / 2;
        let smalls = aa.iter().copied().take(mid).rev().collect::<Vec<_>>();
        let larges = aa.iter().copied().skip(mid).collect::<Vec<_>>();
        let mut ans = larges.iter().map(|&e| 2 * e).sum::<usize>();
        ans -= larges[0];
        ans += smalls[0];
        ans -= smalls.iter().map(|&e| 2 * e).sum::<usize>();
        ans
    } else {
        let mid = n / 2;
        let smalls = aa.iter().copied().take(mid).rev().collect::<Vec<_>>();
        let larges = aa.iter().copied().skip(mid+1).collect::<Vec<_>>();
        let mid = aa[mid];

        let mut temp = larges.iter().map(|&e| 2 * e).sum::<usize>();
        temp -= smalls.iter().map(|&e| 2 * e).sum::<usize>();
        let temp1 = temp + smalls[0] - mid;
        let temp2 = temp - larges[0] + mid;

        std::cmp::max(temp1, temp2)
    };

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