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;

const int maxn = 1e6 + 5;

int f[maxn];
int nope[maxn];
int a[maxn];

int main() {
	int n; scanf("%d", &n);

	for (int i = 1; i <= n; i++) scanf("%d", a+i);

	for (int i = 1; i <= n; i++) {
		int k = a[i];
		f[k]++;
		if (f[k] == 1)
			for (int j = k+k; j < maxn; j += k) nope[j] = 1;
	}
	
	int ans = 0;
	for (int i = 1; i <= n; i++) {
		ans += (f[a[i]] == 1) and !nope[a[i]];
	}
	printf("%d\n", ans);
}