Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5
24 11 8 3 16

Sample Output 1

3

The integers with the property are 2, 3, and 4.

Sample Input 2

4
5 5 5 5

Sample Output 2

0

Note that there can be multiple equal numbers.

Sample Input 3

10
33 18 45 28 8 19 89 86 2 4

Sample Output 3

5

Solution in C (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <math.h>

int main() {
  int hoge = 2 * pow(10, 5);
  int n, a[hoge], c=0, flg=0;
  scanf("%d\n", &n);
  for (int i=0; i<n; i++) {
    scanf("%d", &a[i]);
  }
  for (int i=0; i<n; i++) {
    flg = 0;
    for (int j=0; j<n; j++) {
      if (a[i] != a[j]) {
        if (a[i] % a[j] != 0) {
          flg++;
        }
      }
    }
    if (flg == n-1) {
      c++;
    }
  }
  printf("%d\n", c);
}