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<bits/stdc++.h>
using namespace std;
int a[200010],b[1000005],p,n,m,ans;
int main(){
	cin>>n;
	for(int i=1;i<=n;i++)cin>>a[i],b[a[i]]++;
	for(int i=1;i<=n;i++){
		b[a[i-1]]++,b[a[i]]--;
		int fl=1;
		for(int j=1;j*j<=a[i];j++)
		    if(a[i]%j==0){
		    	if(b[j]>0||b[a[i]/j]>0){
		    		fl=0;break;
		    	}
		    }
		if(fl)ans++;
	}
	printf("%d\n",ans);
	return 0;
}