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,ans,maxn;
int a[200005],g[1000005];
bool f[1000005];
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&a[i]);
		g[a[i]]++;
		maxn=max(maxn,a[i]);
	}
	for(int i=1;i<=n;i++)
		for(int j=a[i]+a[i];j<=maxn;j+=a[i])
			f[j]=true;
	for(int i=1;i<=n;i++)
		if(!f[a[i]]&&g[a[i]]==1)
			ans++;
	cout<<ans<<endl;
	return 0;
}