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<iostream>
using namespace std;
int N,A[2<<17];
int cnt[1<<20];
int main()
{
	cin>>N;
	for(int i=0;i<N;i++)
	{
		cin>>A[i];
		cnt[A[i]]++;
	}
	int ans=0;
	for(int i=0;i<N;i++)
	{
		bool now=true;
		cnt[A[i]]--;
		for(int j=1;j*j<=A[i];j++)
		{
			if(A[i]%j==0)
			{
				if(cnt[j]||cnt[A[i]/j])
				{
					now=false;
					break;
				}
			}
		}
		cnt[A[i]]++;
		ans+=now;
	}
	cout<<ans<<endl;
}
