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;
typedef long long ll;
#define int ll
int32_t main()
{
	int n;
	cin>>n;
	int a[n];
	for(int i=0;i<n;i++)cin>>a[i];
	sort(a,a+n);
	int mx=*max_element(a,a+n);
	vector<int> dp(mx+10);
	for(int i=0;i<n;i++)dp[a[i]]++;
	
	for(int i=1;i<=mx;i++)
	{
		for(int j=2*i;j<=mx;j+=i)
		dp[j]+=dp[i];
	}
	
	int ans=0;
	for(int i=0;i<n;i++)if(dp[a[i]]==1)ans++;
	cout<<ans;
}