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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;


const int Mx = 1000005;

int main() {
	int res=0;
	int nn;
	cin >> nn;
	vector<int> aa(nn);
	vector<int> cnt(Mx);
	rep(i,nn) cin >> aa[i];
	
	sort(aa.begin(),aa.end());
	
	for(int a : aa){
		if(cnt[a]>=2) continue;
		for(int i=a;i<Mx;i+=a){
			cnt[i]++;
		}
	}
	
	rep(i,nn){
		if(cnt[aa[i]]==1) res++;
	}
	
	
	cout << res << endl;
	
	

}