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;

fn main() {
    input! {
        n: i32,
        a: [i64; n],
    }
    let max = 1000001;

    let mut counter: Vec::<i64> = vec![0; max];

    for num in &a {
        let mut base = *num as usize;
        if counter[base] > 0 {
            counter[base] += 1;
            continue;
        }
        while base < max {
            counter[base] += 1;
            base += *num as usize;
        }
    }
    println!("{}", a.iter().filter(|n| counter[**n as usize] == 1).count());
}