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;
typedef long long ll;
int main() {
	int N;
	cin >> N;
	vector<int> A(N);
	for (auto& x : A) cin >> x;
	map<int,int> a;
	for (auto x : A) ++ a[x];
	const int M = 1000000;
	vector<bool> sieve(M+1);
	int r = 0;
	for (auto p : a) {
		int i = p.first;
		if (!sieve[i]) {
			if (p.second == 1) ++ r;
			for (int j = i; j <= M; j += i) sieve[j] = true;
		}
	}
	cout << r << endl;
}
