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 main()
{
	int n;
	cin>>n;
	int a[n+1];
	map<int,int> m;
	for(int i=1;i<=n;++i)
	{
		cin>>a[i];
		m[a[i]]++;
	}
	sort(a+1,a+n+1);
	bool b[a[n]+10];
	memset(b,true,sizeof(b));
	for(int i=1;i<=n;i++)
		if(b[a[i]])
			for(int j=a[i]+a[i];j<=a[n];j+=a[i])
				b[j]=0;
	int ans=0;
	for(int i=1;i<=n;i++)
		if(m[a[i]]<=1&&b[a[i]])
			ans++;
	cout<<ans<<endl;
	return 0;
}
