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<cstdio>
const int maxn=1e6+1;
int vis[maxn],a[maxn],n,ans;
int main(){
  scanf("%d",&n);
  for(int i=1;i<=n;i++)scanf("%d",a+i),vis[a[i]]++;
  for(int i=1;i<=n;i++){
    if(a[i]==1){ans+=(vis[1]==1);continue;}
    if(vis[a[i]]>1||vis[1]>0)continue;bool v=1;
    for(int j=2;j*j<=a[i];j++){
      if(a[i]%j==0){
        v&=(vis[j]==0)&(vis[a[i]/j]==0);
      }
    }
    ans+=v;
  }
  printf("%d\n",ans);
}