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

int main()
{
	int n;
	cin >> n;
	vector<int>a(n);
	vector<int>f(1000005);
	int mx = 0;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
		f[a[i]]++;
		mx = max(mx, a[i]);
	}
	int ans = 0;
	sort(a.begin(), a.end());
	for (int i = 0; i < n; i++) {
		int x = a[i];
		if (f[x] == 1)ans++;
		for (int j = 2; x * j <= mx; j++)
			f[x * j] = 0;
	}
	cout << ans;
		
	
	
}