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];
bool flag[1000010];
vector<int> pr;

int main(){
	int n,i,j;
	cin>>n;
	for(i=0;i<n;i++)
		cin>>a[i];
		
	sort(a,a+n);
	
	for(i=0;i<n;i++){
		if(i && a[i]==a[i-1] && pr.size() && pr[pr.size()-1]==a[i])
			pr.pop_back();
		if(!flag[a[i]]){
			pr.push_back(a[i]);
			for(j=a[i];j<=1000000;j+=a[i])
				flag[j]=true;
		}
	}
	
	cout<<pr.size();
	return 0;
}