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;
int main() {
	int n;
	cin >>n;
	vector<int> a(n);
	vector<int> kol(1010101);
	for (int i = 0; i < n; i++)
		cin >>a[i];
	sort(a.begin(), a.end());
	for (int to : a) {
		if (kol[to] != 0) {
			kol[to] = 2;
			continue;
		}
		for (int i = to; i < 1010101; i += to) 
			kol[i]++;
	}
	int ans = 0;
	for (int to : a) {
		if (kol[to] == 1) ans++;
	}
	cout <<ans;
}