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;

using ll = long long;

const int N = 2e5 + 5;
const int M = 1e6 + 5;
int n;
int a[N], d[M];

int main() {
	cin>>n;
	
	for (int i = 1; i <= n; i++) {
		cin>>a[i];
		if (!d[a[i]]) {
			for (int j = a[i]; j <= 1e6; j += a[i]) 
			d[j]++;
		}
		else {
			d[a[i]]++;
		}
	}
	int ans = 0;
	for (int i = 1; i <= n; i++) if (d[a[i]] == 1) ans++;
	printf("%d\n", ans);
}
