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 JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

const main = (input) => {
  const args = input.trim().split("\n");
  const Ai = args[1]
    .trim()
    .split(" ")
    .map((n) => parseInt(n, 10));
 
  const isNotDividable = (ai, i) => {
    // const Aj = Ai.filter((_, j) => j !== i);
    let Aj = [...Ai];
    Aj.splice(i, 1);
    return Aj.every((aj) => ai % aj !== 0);
  };
 
  const count = Ai.filter((ai, i) => isNotDividable(ai, i)).filter((b) => b).length;
 
  console.log(count);
};
 
main(require("fs").readFileSync("/dev/stdin", "utf8"));