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 <iostream>
#include <vector>

using namespace std;

int b[1000001];

int main(){
  int n;
  cin >> n;
  vector<int> a(n);
  
  for(int i = 0; n > i; i++){
    cin >> a[i];
  	b[a[i]]++;
  }
  
  int ans = 0;
  
  for(int i = 0; 1000001 > i; i++){
    if(b[i] == 1)
	    ans += b[i];
  	if(b[i] > 0){
    	for(int j = i;1000001 > j; j += i)
        	b[j] = 0;
    }
  }
  
  cout << ans << endl;
  return 0;
}