#include <iostream>
#include <algorithm>
using namespace std;
 
int b[1000001];
int ans;
int main () {
	int n;
	cin >> n;
	int a[n];
	for(int i=0;i<n;i++) {
		cin >> a[i];
	}
	sort(a,a+n);
	for(int i=0;i<n;i++) {
		if(b[a[i]]==0) {
			if (a[i]!=a[i-1]&&a[i]!=a[i+1]) {
				ans++;
			}
			for(int j=a[i];j<1000001;j+=a[i]) {
				b[j]=1;
			}
		}
	}
	cout << ans;
}
### Prompt

Create a solution in cpp for the following problem:

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

### Response

```cpp
#include <iostream>
#include <algorithm>
using namespace std;
 
int b[1000001];
int ans;
int main () {
	int n;
	cin >> n;
	int a[n];
	for(int i=0;i<n;i++) {
		cin >> a[i];
	}
	sort(a,a+n);
	for(int i=0;i<n;i++) {
		if(b[a[i]]==0) {
			if (a[i]!=a[i-1]&&a[i]!=a[i+1]) {
				ans++;
			}
			for(int j=a[i];j<1000001;j+=a[i]) {
				b[j]=1;
			}
		}
	}
	cout << ans;
}
```