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
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<stdio.h>
using namespace std;
int A[1000001],v[200001],ans;
int main(){
  int N;
  scanf("%d",&N);
  for(int i=0;i<N;++i){
    scanf("%d",&v[i]);
    A[v[i]]++;
  }
  for(int i=1;i<1000001;++i){
    if(A[i]){
      for(int j=i<<1;j<1000001;j+=i){
        A[j]=0;
      }
    }
  }
  for(int i=0;i<N;++i){
    ans+=A[v[i]]==1;
  }
  printf("%d\n",ans);
}