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 ll long long int

int main(){
	ll n;
	cin>>n;
	vector<ll> v(n);
	vector<int> a((1e6+5),0);
	for(int i=0;i<n;i++){
		cin>>v[i];
		if(a[v[i]]==0){
			for(ll j=v[i];j<a.size();j+=v[i])a[j]++;
		}
		else{
			a[v[i]]++;
		}
	}
	ll ans=0;
	for(int i=0;i<v.size();i++){
		if(a[v[i]]==1)ans++;
	}
	cout<<ans<<endl;
	return 0;
}
