#include <bits/stdc++.h>
using namespace std;
const int L = 1e6;
int main()
  {int N; cin >> N;
  vector<int> A(N); map<int, int> m; for (auto &a : A) {cin >> a; ++m[a];}
  vector<bool> bs(L + 1, true);
  for (auto [i, c] : m) for (int j = i + (c < 2) * i; j <= L; j += i) bs[j] = false;
  int ans = 0; for (auto a: A) ans += bs[a];
  cout << ans << endl;}
### Prompt

Construct a cpp code solution to the problem outlined:

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 L = 1e6;
int main()
  {int N; cin >> N;
  vector<int> A(N); map<int, int> m; for (auto &a : A) {cin >> a; ++m[a];}
  vector<bool> bs(L + 1, true);
  for (auto [i, c] : m) for (int j = i + (c < 2) * i; j <= L; j += i) bs[j] = false;
  int ans = 0; for (auto a: A) ans += bs[a];
  cout << ans << endl;}
```