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;
	cin>>n;
	vector<int> arr(1000001);
	for(int i=0;i<n;i++){
		int a;cin>>a;
		arr[a]++;
	}
	int count=0;
	for(int i=1;i<1000001;i++){
		if(arr[i]){
			if(arr[i]==1) count++;
			for(int j=i;j<1000001;j+=i){
				arr[j]=0;
			}
		}
	}
	
	cout<<count;
	
}
