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 coef(list: &Vec<i32>, reverse: bool) -> Vec<i32> {
    
    let mut ret = Vec::new();
    let n = list.len();
    
    if n % 2 == 0 {
        
        for i in 0..n {
            
            if i == 0 {
                
                ret.push(1);
            } else if i == n - 1 {
                
                ret.push(-1);
            } else if i % 2 != 0 {
                
                ret.push(-2);
            } else {
                
                ret.push(2);
            }
        }
    } else {
        
        for i in 0..n {
            
            if i == 0 || i == n - 1 {
                
                ret.push(1);
            } else if i % 2 != 0 {
                
                ret.push(-2);
            } else {
                
                ret.push(2);
            }
        }
    }
    
    if reverse {
        
        let mut rev = Vec::new();
        for v in ret {
            
            rev.push(v - v * 2);
        }
        
        return rev;
    }
    
    ret
}

fn main() {
    
    let n: i32 = read();
    
    let mut a = Vec::new();
    
    for _x in 0..n {
        
        let b: i32 = read();
        a.push(b);
    }
    
    a.sort();
    
    let mut test1 = coef(&a, false);
    let mut test2 = coef(&a, true);
    
    test1.sort();
    test2.sort();
    
    let mut res1: i64 = 0;
    let mut res2: i64 = 0;
    
    for i in 0..n {
        
        res1 += (a[i as usize] * test1[i as usize]) as i64;
    }
    
    for i in 0..n {
        
        res2 += (a[i as usize] * test2[i as usize]) as i64;
    }
    
    println!("{}", std::cmp::max(res1, res2));
}