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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int length = sc.nextInt();
		int[] nums = new int[length];
		for (int i = 0; i < nums.length; i++) {
			nums[i] = sc.nextInt();
		}
		
		//探索リストを作る
		int[] targets = new int[1000001];
		Arrays.fill(targets, 0);
		
		//入力配列をなめて、探索リストに対して、要素の倍数のインデックスに対してインクリメント
		//上記操作が終わったら、探索リストの要素が1のものが対象の数値
		for (int i = 0; i < nums.length; i++) {
			int num = nums[i];
			if(targets[num] != 0) {
				targets[num] = 2;
				continue;
			}
			for(int j = num; j <= 1000000; j+=num) {
				targets[j]++;
			}
		}
		int count = 0;
		for (int i = 0; i < nums.length; i++) {
			if(targets[nums[i]] == 1) {
				count++;
			}
		}
		System.out.println(count);
	}
}