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)

fn main() {
    proconio::input! {
        n: usize,
        mut a: [i32;n],
    }
    let mut t=0;
    let mut s=std::collections::BTreeSet::new();
    a.sort();
    for i in 1..n {
        if a[i-1]==a[i] {
            s.insert(a[i]);
        }
    }
    for a in a {
        let mut v=vec![];
        let mut x=a;
        let mut i=2;
        while x>=i*i {
            while x%i==0 {
                v.push(i);
                x/=i;
            }
            i+=1;
        }
        if x>1 {
            v.push(x);
        }
        let mut f=true;
        for b in 1..(1<<v.len())as u32 {
            let mut w=1;
            let mut c=b;
            while c>0 {
                w*=v[c.trailing_zeros()as usize];
                c&=c-1;
            }
            if s.contains(&w) {
                f=false;
                break;
            }
        }
        if f {
            t+=1;
        }
        s.insert(a);
    }
    println!("{}",t);
}