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;

#define MAXN 200010

int n,a[MAXN],cnt[1000010],f[1000010];

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
	{
		scanf("%d",a+i);
		++cnt[a[i]];
	}
	for(int i=1;i<=1000000;++i)
	{
		if(!cnt[i])continue;
		for(int j=i;j<=1000000;j+=i)
			f[j]+=cnt[i];
	}
	int ans=0;
	for(int i=1;i<=n;++i)
	{
		if(f[a[i]]==1)++ans;
	}
	printf("%d\n",ans);
}