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

int const N = 1e6+1;
int a[N];

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int n;
    for (cin >> n; n--;) {
        int x;
        cin >> x;
        a[x]++;
    }
    for (int i = 1; i < N; i++) if (a[i]) {
        for (int j = i * 2; j < N; j += i)
            a[j] = 0;
    }
    cout << count(a + 1, a + N, 1) << '\n';
    return 0;
}

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

int const N = 1e6+1;
int a[N];

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int n;
    for (cin >> n; n--;) {
        int x;
        cin >> x;
        a[x]++;
    }
    for (int i = 1; i < N; i++) if (a[i]) {
        for (int j = i * 2; j < N; j += i)
            a[j] = 0;
    }
    cout << count(a + 1, a + N, 1) << '\n';
    return 0;
}

```