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
#include <iostream>
using namespace std;

int n, a[200005], v[1000005], mx;

int main() {
    cin >> n;
    for(int i =1; i <= n; i++) {
        cin >> a[i];
        mx = max(mx, a[i]);
    }
    for(int i = 1; i <= n; i++)
        for(int j = a[i]; j <= mx; j += a[i])
            v[j]++;

    int ans = 0;
    for(int i = 1; i <= n; i++)
        if(v[a[i]] == 1)
            ans++;
    cout << ans;
}
