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(){
	bool arr[(int)1e6+1]={};
	int N,ipt[(int)2e5];
	cin>>N;
	for(int i=0; i<N; i++)cin>>ipt[i];
	sort(ipt,ipt+N);
	int cnt=0;
	for(int i=0; i<N-1; i++){
		if(arr[ipt[i]]==0){
			if(ipt[i]!=ipt[i+1])cnt++;
			for(int j=ipt[i]; j<=ipt[N-1]; j+=ipt[i])arr[j]=1;
		}
	}if(arr[ipt[N-1]]==0)cnt++;
	cout<<cnt<<'\n';
}