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 n,a[200004],ans;
bool iss[1000004];
int main(){
	cin>>n;
	for(int i=2;i<=n+1;i++)cin>>a[i];sort(a+2,a+2+n);
	for(int i=2;i<=n+1;i++){
		if(!iss[a[i]])ans++;
		if(a[i]==a[i-1]){
			if(!iss[a[i]]){
				ans--;
				if(a[i]!=a[i-2])ans--;
			}
		}else{
			if(!iss[a[i]])for(int j=a[i]*2;j<=1e6;j+=a[i])iss[j]=1;
		}
	}
	cout<<ans;
}