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 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] as = new int[n];
		int[] count = new int[1000001];
		boolean[] hantei = new boolean[1000001];
		for(int i=0; i<n; i++){
			as[i] = sc.nextInt();
			count[as[i]]++;
		}
		for(int i=0; i<n; i++){
			if(count[as[i]] >= 2){
				int j = 2;
				int tmp = as[i];
				while(tmp <= 1000000){
					hantei[tmp] = true;
					tmp = as[i]*j;
					j++;
				}
			} else if(count[as[i]] >= 1){
				int j = 2;
				int tmp = as[i]*j;
				while(tmp <= 1000000){
					hantei[tmp] = true;
					j++;
					tmp = as[i]*j;
				}
			}
		}
		int ans = 0;
		for(int a: as){
			if(!hantei[a]) ans++;
		}
		System.out.println(ans);

	}
}