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::{input};
// use std::collections::HashSet;

fn main() {
    input! {
        n: usize,
        mut a: [usize; n]
    }

    let mut devide_array: [usize; 1_000_001] = [0; 1_000_001];

    a.sort();

    for &a_i in &a {
        if devide_array[a_i] != 0 {
            devide_array[a_i] = 2;
            continue;
        }
        for j in 1..=(1_000_001/a_i) {
            devide_array[j * a_i] += 1;
        }
    }

    let mut res = 0;

    for a_i in a {
        if devide_array[a_i] == 1 {
            res += 1;
        }
    }

    // let mut invalid_ids = HashSet::new();
    // 'outer: for i in 0..a.len() {
    //     for j in 0..a.len() {
    //         if i <= j && a[i] != a[j] {
    //             break;
    //         } else if (i != j) && (a[i] % a[j] == 0) {
    //             invalid_ids.insert(i);
    //             continue 'outer;
    //         } else if invalid_ids.contains(&j) {
    //             continue;
    //         }
    //     }
    //     res += 1;
    // }

    println!("{}", res);
}