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::*;
use std::collections::*;

#[fastout]
fn main() {
    input! {
        n: usize,
        a: [usize; n],
    }

    let mut ok = vec![false; 1000001];
    let mut cnt = vec![0; 1000001];
    for b in a {
        ok[b] = true;
        cnt[b] += 1;
    }

    let mut ans = 0;
    for i in 0..=1000000 {
        if cnt[i] > 1 {
            ok[i] = false;
        }
        if !ok[i] {
            continue;
        }
        ans += 1;
        for j in 2.. {
            if i * j > 1000000 {
                break;
            }
            ok[i * j] = false;
        }
    }

    println!("{}", ans);
}