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;
#define ll long long
int main(){
	ll n;
	cin>>n;
	ll arr[n];
	int cnt[1000002]={0};
	bool vis[1000002]={0};
	for(int i=0;i<n;i++) {
		cin>>arr[i];
		cnt[arr[i]]++;
		if(vis[arr[i]]==0&&cnt[arr[i]]==1){
		for(int j=2*arr[i];j<=1000000;j+=arr[i]){
			vis[j]=1;
		}
		}
	}
	ll ans=0;
	for(int i=0;i<n;i++){
		if(vis[arr[i]]==0&&cnt[arr[i]]==1){
			ans++;
		}
	}
	cout<<ans;
	return 0;
}