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;

const int M = 1000000;
int n;
int a[200000];
bool c[M + 1];
int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> a[i];
  sort(a, a + n);
  int cnt = 0;
  for (int i = 0; i < n; ++i) {
    if (c[a[i]]) continue;
    if (i == n - 1 || a[i + 1] != a[i]) {
      ++cnt;
    }
    for (int p = a[i]; p <= M; p += a[i]) {
      c[p] = true;
    }
  }
  cout << cnt << endl;
}
