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 input::Input;

fn main() {
    let mut input = Input::default();

    let n = input.parse();
    let mut a = (0..n).map(|_| input.parse()).collect::<Vec<usize>>();
    a.sort();

    let mut b = vec![true; 1000001];
    let mut c = vec![0u32; 1000001];
    let mut ans = 0;
    if a[0] != 1 {
        for i in 0..n {
            if b[a[i]] || c[a[i]] > 0 {
                c[a[i]] += 1;
            }

            if b[a[i]] {
                let mut j = 1;
                while a[i] * j <= 1000000 {
                    b[a[i] * j] = false;
                    j += 1;
                }
                ans += 1;
            }
        }
        ans -= c.iter().filter(|x| **x > 1).count();
    }
    println!("{}", ans);
}

#[allow(dead_code)]
pub mod input {
    #[derive(Default)]
    pub struct Input(Vec<String>);

    impl Input {
        pub fn read_line(&mut self) -> String {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).ok().expect("read error");
            s
        }
        pub fn parse<T: std::str::FromStr>(&mut self) -> T {
            let x = if let Some(x) = self.0.pop() {
                x
            } else {
                let s = self.read_line();
                self.0 = s.split_whitespace().map(String::from).rev().collect();
                self.0.pop().expect("reached EOF")
            };
            x.parse().ok().expect("parse error")
        }
    }
}