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: Runtime Error)

use proconio::*;

fn main() {
    input! {
        n: i32,
    }

    let mut v = vec![];
    for _ in 0..n {
        input! {
            x: i32,
        }

        v.push(x);
    }

    let mut p = [0; 60001];
    for i in 0..n as usize {
        p[v[i] as usize] += 1;
    }

    for i in 0..3001 {
        if p[i] == 0 {
            continue;
        }

        for j in 2..60001/i {
            p[i * j] = 0;
        }
    }

    let ans: i32 = p.iter().map(|&x| if x == 1 {1} else {0}).sum();
    println!("{}", ans);
}