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)

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 read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
fn main(){
    let n:usize  =read();
    let mut an = vec![];
    for _ in 0..n{
        an.push(read::<i64>());
    }
    an.sort();
    let mut bn:Vec<i64> = (0..n).map(|x| {
        if n % 2 == 0{
            even(x,n-1)
        } else {
            odd(x,n-1)
        }
    }).collect();
    let mut cn:Vec<i64> = (0..n).map(|x| {
        if n % 2 == 0{
            even_1(x,n-1)
        } else {
            odd_1(x,n-1)
        }
    }).collect();
    bn.sort();
    cn.sort();
    let  up:Vec<i64> = an.iter().zip(bn.into_iter()).map(|(a,b)| {a*b}).collect();
    let down:Vec<i64> = an.iter().zip(cn.into_iter()).map(|(a,b)| {a*b}).collect();
    // println!("{:?}",up );
    // println!("{:?}",down );
    let ans = std::cmp::max(up.into_iter().sum::<i64>(),down.into_iter().sum::<i64>());
    println!("{}", ans);
}
fn odd(x:usize,upper:usize)->i64{
        if x == 0 || x == upper{
            1
        } else if x % 2 == 0 {
            2
        } else {
            -2
        }
}
fn odd_1(x:usize,upper:usize)->i64{
        if x == 0 || x == upper{
            -1
        } else if x % 2 == 0 {
            -2
        } else {
            2
        }
}
fn even(x:usize,upper:usize)->i64{
    if x == 0 {
        1
    } else if x == upper {
        -1
    } else if x % 2 == 0{
        2
    } else {
        -2 
    }
}
fn even_1(x:usize,upper:usize)->i64{
    if x == 0 {
        -1
    } else if x == upper {
        1
    } else if x % 2 == 0{
        -2
    } else {
        2 
    }
}