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;
const int N=2e5+100,M=1e6+100;
int n,num;
int a[N],mark[M];
inline void solve(int x)
{
	mark[x]--;
	for (int i=1;i*i<=x;i++)
	if (x%i==0)
	if (mark[i]||mark[x/i])
	{
		mark[x]++;
		return ;
	}
	num++;
	mark[x]++;
	return ;
}
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%d",a+i);
		mark[a[i]]++;
	}
	for (int i=1;i<=n;i++) solve(a[i]);
	printf("%d\n",num);
	return 0;
}