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 M=1e6+6;

int co[M];
int n;

int main()
{
	cin >> n;
	for(int i=0;i<n;i++)
	{
		int x;
		cin >> x;
		co[x]++;
	}
	int ans=0;
	for(int i=1;i<M;i++)
	{
		if(co[i]==0) continue;
		for(int j=2*i;j<M;j+=i)
			co[j]=0;
		ans+=co[i]==1;
	}
	cout << ans << endl;
}