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;

bool flg[1000010];
int cnt[1000010];

int main() {
	int n; cin >> n;
	int a[n];
	for(int i = 0; i < n; ++i) {
		cin >> a[i];
		++cnt[a[i]];
	}
	sort(a, a + n);
	int ans = 0;
	for(int i = 0; i < n; ++i) {
		if(flg[a[i]]) continue;
		if(cnt[a[i]] < 2) ++ans;
		for(int j = a[i]; j < 1000010; j += a[i]) {
			flg[j] |= true;
		}
	}
	cout << ans << '\n';
	return 0;
}