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
	import java.util.*;
	import java.util.Map.Entry;
	 
	 
	 class Main {
		 static int mod =  (int) (Math.pow(10,9)+7);
//		 static int mod =  (int) 998244353;
		 public static void main(String[] args) {
	    	
	        Scanner sc = new Scanner(System.in);

	        int N = sc.nextInt();
	        int H = 1000000;
	        int[] m = new int[1000005];
	        for(int i=0;i<N;i++) {
	        	m[sc.nextInt()]++;
	        }
	        long ans=0;
	        for(int i=1;i<=H+3;i++) {
	        	if(m[i]!=0) {
		        	if(m[i]==1)ans++; 
	        		for(int j=i+i;j<H+5;j=j+i) {
	        			if(m[j]==1)m[j]=0;
	        		}	        		
	        	}
	        }
	        
	        System.out.println(ans);
	    }
	}