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

const int MAXN = 2e5+4;
int a[MAXN];
const int MAXM = 1e6;
bool flag[MAXM+4];

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

	sort(a+1, a+n+1);

	int ans = 0;
	for (int i=1; i<=n; i++) {
		if (false==flag[a[i]]) {
			if (a[i]!=a[i+1]) {

				ans++;
			}

			for (int j=1; a[i]*j<=MAXM; j++) {
				flag[a[i]*j] = true;
			}
		}
	}

cout<<ans<<"\n";


}