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;

int main(){
	map<int,int> a;
	int n;
	cin>>n;
	for(int i=0;i<n;i++){
		int d;
		cin>>d;
		a[d]++;
	}
	bool seive[(int)1e6+30]={};
	for(auto &f:a){
		int temp = f.first;
		if(f.second!=1) seive[temp]=true;
		for(int i=temp*2;i<=1e6+20;i+=temp){
			seive[i]=true;
		}
	}
	int result=0;
	for(auto &f:a){
		if(!seive[f.first]){
			result++;
		}
	}
	cout<<result<<"\n";

}