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)

use proconio::{input, fastout};

#[fastout]
fn main() {
    input! {
        n: usize,
        mut a: [usize; n],
    }
    a.sort();
    let amax = a[n-1];
    let mut f = vec![false; amax + 1];
    let mut ans = 0;
    for i in 0..n {
        if f[a[i]] {continue;}
        let mut j = a[i];
        if i+1 == n || a[i] != a[i+1] {ans += 1;}
        while j <= amax {
            f[j] = true;
            j += a[i];
        }
    }
    println!("{}", ans);
}