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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int,int>;

const	int m = 1000005;

int main(){
	int n;
	cin >> n;
	vector<int> a(n);
	rep(i,n) cin >> a[i];
	vector<int> cnt(m);
	for(int x : a){
		if(cnt[x] != 0){
			cnt[x] = 2;
			continue;
		}
		for(int i = x; i < m; i += x) cnt[i]++;
	}
int ans = 0;
for(int x : a){
	if(cnt[x] == 1) ans++;
} 
cout << ans << endl;
}