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 ll long long
using namespace std;

const int maxx=1e6+5;
ll a[maxx];
int n,i,ans,j,x;

int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	scanf("%d",&n);
	while(n--){
		scanf("%d",&x);
		a[x]++;
	}
	vector<bool> dv(maxx,true);
	
	for(i=1;i<=maxx;i++){
		if(!a[i]) continue;
		if(a[i]==1&&dv[i]) ans++;
		for(j=2;i*j<maxx;j++) dv[i*j]=false;
	}
	
	printf("%d\n",ans);
	return 0;
}