#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
using namespace std;

int main() {
	int N;
	cin >> N;
	vector<int> Nums(1000001,0);
	for (int i = 0; i < N; i++) {
		int A;
		cin >> A;
		Nums[A]++;
	}
	int ans = 0;
	for (int i = 1; i <= 1000000; i++) {
		if (Nums[i] >= 1) {
			if (Nums[i]==1) ans++;
			int k = i * 2;
			while (k <= 1000000) {
				Nums[k] = 0;
				k += i;
			}
		}
	}
	cout << ans << endl;

}
### Prompt

Please provide a CPP coded solution to the problem described below:

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 <vector>
#include <algorithm>
#include <set>
using namespace std;

int main() {
	int N;
	cin >> N;
	vector<int> Nums(1000001,0);
	for (int i = 0; i < N; i++) {
		int A;
		cin >> A;
		Nums[A]++;
	}
	int ans = 0;
	for (int i = 1; i <= 1000000; i++) {
		if (Nums[i] >= 1) {
			if (Nums[i]==1) ans++;
			int k = i * 2;
			while (k <= 1000000) {
				Nums[k] = 0;
				k += i;
			}
		}
	}
	cout << ans << endl;

}
```