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;
bool pp[1000005],used[1000005];
int a[200001]; 
int main()
{
	int n;
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>a[i];
	for(int i=1;i<=n;i++)
	{
		if(used[a[i]]==1)
			pp[a[i]]=1;
		used[a[i]]=1;
		if(pp[a[i]]==0)
			for(int j=a[i]*2;j<=1000000;j+=a[i])
				pp[j]=1;
	}
	int ans=0;
	for(int i=1;i<=n;i++)
		if(!pp[a[i]])
			ans++;
	cout<<ans; 
	return 0;
}
