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 maxn=1000005;
int n,ans;
int cnt[1000*1000+5];
int main()
{
    cin >> n;
    int a[n+1];
    for(int i=1;i<=n;i++)cin>>a[i];
    for(int i=1;i<=n;i++)
	{
       if(cnt[a[i]])
	   {
        	cnt[a[i]]=2;
        	continue;
       }
       int val=a[i];
       for(int j=val;j<maxn;j+=val)cnt[j]++;
   }
    for(int i=1;i<=n;i++)if(cnt[a[i]]<=1)ans++; 
    cout<<ans;
	return 0;
}