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 i64 = long long;
#define endl "\n"

int main()
{
  i64 N;
  cin >> N;
  vector<i64> A(1000001);
  for (i64 i = 0; i < N; i++)
  {
    i64 a;
    cin >> a;
    A[a]++;
  }
  i64 ans = 0;
  for (i64 i = 0; i < 1000001; i++)
  {
    if (A[i] == 0)
      continue;
    if (A[i] == 1)
      ans++;
    for (i64 j = i * 2; j < 1000001; j += i)
      A[j] = 0;
  }
  cout << ans << endl;
  return 0;
}
