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::input;

fn main() {
    input! {
        n:isize,
        mut ar: [i32; n]
    }

    ar.sort();
    let mut num = [0; 1_000_001];
    for i in 0..ar.len() {
        num[ar[i] as usize] += 1;
    }

    let mut res = 0;
    for i in 0..ar.len() {
        if num[ar[i] as usize] > 1 {
            continue;
            // 複数存在するため
        }
        let mut f = true;
        for x in 1..(ar[i] as f64).sqrt() as i32 + 1 {
            if ar[i] % x == 0 {
                if num[x as usize] > 0 {
                    f = false;
                }
                if x > 1 && num[(ar[i] / x) as usize] > 0 {
                    f = false;
                }
            }
        }

        if f {
            res += 1;
        }
    }
    println!("{}", res);
}