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
#include <stdio.h>

int count[1000010],check[1000010],x[200010];
int main()
{
	int a;
	scanf("%d",&a);
	for(int i=1;i<=a;i++) scanf("%d",&x[i]);
	for(int i=1;i<=a;i++) count[x[i]]++;
	
	int ans = 0;
	for(int i=1;i<=1000000;i++)
	{
		if(count[i]>0)
		{
			if(count[i]==1 && check[i]==0) ans++;
			for(int j=i;j<=1000000;j+=i) check[j] = 1;
		}
	}
	printf("%d",ans);
}