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 ll = long long;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)


signed main() {
  int n;
  cin >> n;
  vector<int> a(n);
  rep(i,n) cin >> a[i];
  int mx = 0;
  rep(i,n) mx = max(mx, a[i]);

  vector<int> c(mx+1);
  rep(i,n) {
    for(int j=1; j * a[i] <= mx; j++) {
      c[j*a[i]]++;
    }
  }
  int ans = 0;
  rep(i,n) ans += (c[a[i]]==1);
  cout << ans << endl;
}
