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>
#define int long long
using namespace std;
int n,a[200001],ans,pd[1000001];
bool cmp(int x,int y)
{
	return x<y;
}
void zh(int x)
{
	for(int i=x;i<=1000000;i+=x)
	pd[i]=1;
}
signed main()
{
	scanf("%lld",&n);
	for(int i=1;i<=n;i++)
	scanf("%lld",&a[i]);
	sort(a+1,a+n+1,cmp);
	for(int i=1;i<=n;i++)
	if(pd[a[i]]==0)
	{
		if(a[i]!=a[i+1])
		ans++;
		zh(a[i]);
	}
	printf("%lld",ans);
    return 0;
}