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(void){

  int i,j,flag = 0,count = 0;
  int n,*a;
  scanf("%d",&n);
  a = (int*)malloc(sizeof(int)*n);
  
  for(i=0;i<n;i++){
    scanf("%d",&a[i]);
  }
 
  for(i=0;i<n;i++){
   for(j=0;j<n;j++){
   
     if(i != j){
       if(a[i] >= a[j] && a[i] % a[j] == 0){
         flag = 1;
         break;
       }
     }
   }   
    
     if(flag==0){
      count++;
     }     
    flag = 0;
       
  }
  
       printf("%d",count);
  
 free(a);
 return 0; 
}