Problem:
Score : 400 points

Problem Statement

Given is a number sequence A of length N.

Find the number of integers i \left(1 \leq i \leq N\right) with the following property:

For every integer j \left(1 \leq j \leq N\right) such that i \neq j , A_j does not divide A_i.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the answer.

Sample Input 1

5
24 11 8 3 16

Sample Output 1

3

The integers with the property are 2, 3, and 4.

Sample Input 2

4
5 5 5 5

Sample Output 2

0

Note that there can be multiple equal numbers.

Sample Input 3

10
33 18 45 28 8 19 89 86 2 4

Sample Output 3

5

Solution in Rust (1.42.0) (judge verdict: Time Limit Exceeded)

fn main(){
    let n: usize = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        s.trim_end().to_owned().parse().unwrap()
    };
    let mut vec: Vec<i32> = Vec::new();

    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let ws = s.split_whitespace();
    for v in ws {
        let t: i32 = v.parse().unwrap();
        vec.push(t);
    }

    let mut result_vec: Vec<usize> = Vec::new();
    'iloop: for i in 0..n {
        'jloop: for j in 0..n {
            if i == j {
                continue 'jloop;
            }
            if vec.get(i).unwrap() % vec.get(j).unwrap() == 0 {
                continue 'iloop;
            }
        }
        result_vec.push(i + 1);
    }
    result_vec.sort();
    result_vec.dedup();
    println!("{}", result_vec.len());
}