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: Wrong Answer)

use proconio::input;

fn main() {
    input! {
        n: usize,
        mut a: [usize; n],
    }
    a.sort();
    let mut r = Vec::new();
    if a[0] == 1 {
        let ai = a.remove(0);
        if a.contains(&ai) == false {
            r.push(ai);
        }
        a = a.iter().filter(|&aj| *aj != 1).cloned().collect();
    }
    while a.is_empty() == false {
        let ai = a.remove(0);
        if a.contains(&ai) == false {
            r.push(ai);
        }
        let mut x = 1;
        let mut i = 0;
        while i < a.len() && ai * x <= 1000000 {
            if a[i] == ai * x {
                a.remove(i);
            } else if a[i] > ai * x {
                x += 1;
            } else {
                i += 1;
            }
        }
    }
    println!("{}", r.len());
}