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;
using lint = long long int;

int main() {
  lint N;
  cin >> N;

  vector<lint> A(N);
  for(auto& elem : A) cin >> elem;
  set<lint> st(A.begin(), A.end());

  for(auto a : st) {
    for(int i=2; i*a<1123456; i++) {
      st.erase(i*a);
    }
  }

  map<lint, lint> mp;
  for(auto a : A) mp[a]++;
  for(auto [a, cnt] : mp) {
    if(cnt >= 2) st.erase(a);
  }

  cout << st.size() << endl;
}