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.

Examples

Input

5
24 11 8 3 16


Output

3


Input

4
5 5 5 5


Output

0


Input

10
33 18 45 28 8 19 89 86 2 4


Output

5
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;
import java.util.stream.IntStream;

/**
 * 解説通りに実装したソースコード
 */
public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			Map<Integer, Integer> map = new HashMap<>();
			int max = IntStream.range(0, n).map(i -> {
				int a = scanner.nextInt();
				map.put(a, map.getOrDefault(a, 0) + 1);
				return a;
			}).max().getAsInt();
			boolean[] dp = new boolean[max + 1];
			map.keySet().stream().forEach(i -> dp[i] = (1 == map.get(i)));
			map.keySet().stream().sorted().forEach(i -> {
				for (int j = i + i; j <= max; j += i) {
					dp[j] = false;
				}
			});
			System.out.println(IntStream.rangeClosed(0, max).filter(i -> dp[i]).count());
		}
	}
}
