#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e6;

set<int> st;
map<int, bool> repeat, vis;

int main() {
	int n; cin >> n;
	for (int i = 0; i < n; i++) {
		int x; cin >> x;
		if (st.count(x)) repeat[x] = true;
		st.insert(x);
	}
	int ans = 0;
	for (auto i : st) {
		if (vis[i]) continue;
		for (int j = i + i; j <= MAXN; j += i)
			vis[j] = true;
		ans += !repeat[i] and !vis[i];
	}
	cout << ans << "\n";
}
### Prompt

Please formulate a Cpp solution to 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 <bits/stdc++.h>
using namespace std;
const int MAXN = 1e6;

set<int> st;
map<int, bool> repeat, vis;

int main() {
	int n; cin >> n;
	for (int i = 0; i < n; i++) {
		int x; cin >> x;
		if (st.count(x)) repeat[x] = true;
		st.insert(x);
	}
	int ans = 0;
	for (auto i : st) {
		if (vis[i]) continue;
		for (int j = i + i; j <= MAXN; j += i)
			vis[j] = true;
		ans += !repeat[i] and !vis[i];
	}
	cout << ans << "\n";
}
```