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 <algorithm>
#include <iostream>
int n,a[200010];
int m[1000010];
int main(){
	std::cin>>n;
	for(int i=0;i<n;i++){
		std::cin>>a[i];
	}
	std::sort(a,a+n);
	int ans=0;
	for(int i=0;i<n;i++){
		if(!m[a[i]]){
			if(i==n-1||a[i]!=a[i+1])ans++;
			for(int j=a[i];j<=1000000;j+=a[i]){
				m[j]=true;
			}
		}
	}
	std::cout<<ans<<std::endl;
	return 0;
}
