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;

const int maxn=1000002;
int n, ans=0, cnt[maxn+3], divs[maxn+3];

int main(){
	memset(cnt,0,sizeof cnt);
	memset(divs,0,sizeof divs);
	cin >> n;
	for (int i=0;i<n;i++){
		int a;
		cin >> a;
		cnt[a]++;
	}
	for (int i=1;i<=maxn;i++){
		if (cnt[i]>0){
			if (cnt[i]==1 && divs[i]==0) ans++;
			for (int j=i+i;j<=maxn;j+=i) divs[j]++;
		}
	}
	cout << ans << "\n";
}