#include <bits/stdc++.h>
using namespace std;

int arr[200005], ans;
int cnt[2000005];

int main(){ 
	int n;
	cin >> n;
	for(int i = 1;i <= n;i++){
		cin >> arr[i];
		cnt[arr[i]]++;
	}

	for(int i = 1;i <= n;++i){
		if(cnt[arr[i]] > 1 || (cnt[1] && arr[i] != 1) )
			continue;
		bool ok = 1;
		for(int j = 2;j * j <= arr[i];++j){
			if(arr[i] % j != 0)
				continue;
			ok &= ((cnt[j] > 0) || (cnt[arr[i] / j])) ^ 1;
		}
		ans += ok;
	}

	cout << ans;
}
### Prompt

Develop a solution in Cpp 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 <bits/stdc++.h>
using namespace std;

int arr[200005], ans;
int cnt[2000005];

int main(){ 
	int n;
	cin >> n;
	for(int i = 1;i <= n;i++){
		cin >> arr[i];
		cnt[arr[i]]++;
	}

	for(int i = 1;i <= n;++i){
		if(cnt[arr[i]] > 1 || (cnt[1] && arr[i] != 1) )
			continue;
		bool ok = 1;
		for(int j = 2;j * j <= arr[i];++j){
			if(arr[i] % j != 0)
				continue;
			ok &= ((cnt[j] > 0) || (cnt[arr[i] / j])) ^ 1;
		}
		ans += ok;
	}

	cout << ans;
}
```