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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.Scanner;
public class Main {
public static void main(String[] args) {
	Scanner sc = new Scanner(System.in);
	int n = sc.nextInt(),p=0,ans=0;
	int [] a = new int [n];
	for (int  i=0;i<n;i++) {
		a[i]=sc.nextInt();
		if (a[i]==1) p++;
	}
	if (p>0) System.out.println(p);
	else {
		for (int i=0;i<n;i++) {
			boolean d = true;
			for (int j=0;j<n;j++) {
				if (i==j) continue;
				if (a[i]%a[j]==0) {
					d=false;
					break;
				}
			}
			if (d) ans++;
		}
		System.out.println(ans);
	}
	sc.close();}}