#include <bits/stdc++.h>
using namespace std;
int main()
  {int N, ans{}; cin >> N;
  int A[N]; map<int, int>m; set<int> s; for (int &a: A) {cin >> a; ++m[a]; s.insert(a);}
  vector<bool> B(1000001, true); for (int a : s) for (int j{m[a] > 1 ? a : a + a}; j <= 1000000; j += a) B[j] = false;
  for (int a : A) ans += B[a]; 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 main()
  {int N, ans{}; cin >> N;
  int A[N]; map<int, int>m; set<int> s; for (int &a: A) {cin >> a; ++m[a]; s.insert(a);}
  vector<bool> B(1000001, true); for (int a : s) for (int j{m[a] > 1 ? a : a + a}; j <= 1000000; j += a) B[j] = false;
  for (int a : A) ans += B[a]; cout << ans;}
```