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: Accepted)

// https://atcoder.jp/contests/abc170/tasks/abc170_d

use proconio::fastout;
use proconio::input;

#[fastout]
fn main() {
    input! {
        n: usize,
        mut a_s: [usize; n],
    }
    a_s.sort_unstable();
    let a_max = *a_s.last().unwrap();
    let mut dp = vec![0; a_max + 1];
    for &a in &a_s {
        if dp[a] >= 2 {
            continue;
        }
        for j in 1..=a_max {
            let p = j * a;
            if p > a_max {
                break;
            } else {
                dp[p] += 1;
            }
        }
    }
    println!("{}", a_s.iter().filter(|&&x| dp[x] == 1).count());
}