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=2e+5+5;
int a[N];
int n;
map<int,int> mp;

int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		cin>>a[i];
		mp[a[i]]++;
	}
	int ans=0;
	for(auto it:mp)
	{
		if(it.second==1)
			ans++;
		for(int i=2;i*it.first<=1e+6;i++)
		{
			int j=i*it.first;
			if(mp.find(j)!=mp.end())
				mp[j]=0;
		}
	}
	cout<<ans;
}

