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() {
	int n;
	while(cin>>n){
		int num[n];
		int isdiv[int(1e6)+1]={};
		for(int i=0;i<n;i++){
			cin>>num[i];
		}
		sort(num,num+n);
		int cnt=0;
		for(int i=0;i<n-1;i++){
			if(isdiv[num[i]]==0){
				if(num[i]!=num[i+1]){
					cnt++;
				}
				for(int j=num[i];j<=num[n-1];j+=num[i]){
					isdiv[j]=1;
				}
			}
		}
		cout<<cnt+(isdiv[num[n-1]]==0)<<'\n';
	}
}