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 main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int N;
  cin >> N;
  vector<int> A(N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
  }
  vector<int> B(*max_element(A.begin(), A.end()) + 1, 0);
  for (int a : A) {
    for (int b = a; b < (int)B.size(); b += a) {
      B[b]++;
    }
  }
  int res = 0;
  for (int a : A) {
    if (B[a] == 1) res++;
  }
  cout << res << '\n';
  return 0;
}
