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;
use std::collections::HashMap;

fn helper(
  map: &HashMap<usize, usize>,
  val: usize
) -> bool {
  if let Some(v) = map.get(&val) {
    if &1 < v { return false }
  }
  
  let mut i = 2;
  while i * i <= val {
    if val % i == 0 {
      if map.get(&i).is_some() || map.get(&(val / i)).is_some() {
        return false;
      }
    }
    i += 1;
  }
  true
}

fn main() {
  input! {
    n: usize,
    vals: [usize;n]
  };
 
  let mut map = HashMap::new();  
  for i in 0..n {
    let entry = map.entry(vals[i]).or_insert(0);
    *entry += 1;
  }
  
  let mut result = 0;
  for v in vals {
    if helper(&map, v) {
      result += 1;
    }
  }
  println!("{}", result);
}