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> a(n);
	for(int i=0; i<n; ++i) cin >> a[i];
	sort(a.begin(),a.end());

	vector<int> dp(a[n-1]+1,1);
	for(int i=0; i<n; ++i){
		if(dp[a[i]]==0) continue;
		if(i>0 && a[i]==a[i-1]){
			dp[a[i]]=0;
			continue;
		}
		for(int j=2*a[i]; j<=a[n-1]; j+=a[i]){
			dp[j]=0;
		}
	}
	int ans=0;
	for(int i=0; i<n; ++i){
		ans += dp[a[i]];
	}

	cout << ans << endl;
}