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;
	int ma = 0;
	vector<int> av(n);
	for (auto& a : av) {
		cin >> a;
		ma = max(a, ma);
	}

	vector<int> cv(ma + 1, 0);
	for (auto& a : av) {
		int b = a;
		while (b <= ma) {
			++cv[b];
			b += a;
		}
	}

	int ret = 0;
	for (auto& a : av) {
		if (cv[a] == 1) {
			++ret;
		}
	}
	cout << ret << endl;

	return 0;
}