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 <stdlib.h>

int main(){
  int N;
  scanf("%d",&N);
  int p[200000];
  for (int i=0; i<N; i++){
      scanf("%d", p+i);
  }
  int l[200000];
  for (int i=0; i<N; i++){
      l[i] = 1;
  }
  for (int i=1; i<N; i++){
      for (int j=0; j<i; j++){
          if (p[i] % p[j] == 0) l[i] = 0;
          if (p[j] % p[i] == 0) l[j] = 0;
      }
  }
  int c=0;
  for (int i=0; i<N; i++){
      c += l[i];
  }
  printf("%d",c);
  return 0;
}