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 n;
int seq[1000050],a[200050];
int cnt[1000050];

int main()
{
	scanf("%d",&n);
	for(int i = 1;i <= n; ++ i)
	{
		scanf("%d",&a[i]);
		cnt[a[i]] ++;
	}
	for(int i = 1;i <= 1000000; ++ i)
		for(int j = 1;j * i <= 1000000; ++ j)
			seq[j * i] += cnt[i];
	int c = 0;
	for(int i = 1;i <= n; ++ i)
		c += !(seq[a[i]] - 1);
	printf("%d\n",c);
}