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: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args){
		try(Scanner sc = new Scanner(System.in)) {
			
			int n = sc.nextInt();
			
			int[] aArray = new int[n];
			HashMap<Integer, Integer> dupMap = new HashMap<>(); 
			
			for(int i = 0 ; i < n ; i++ ) {
				aArray[i] = sc.nextInt();
				if ( dupMap.containsKey(aArray[i]) ) {
					int current = dupMap.get(aArray[i]);
					dupMap.put(aArray[i], current+1);
				}
				else {
					dupMap.put(aArray[i], 1);
				}
					
			}
			
			long ans = 0;
			
			List<Integer> uniqList = new ArrayList<>(dupMap.keySet());
			Collections.sort(uniqList);
			
			for(int i = 0 ; i < uniqList.size() ; i++ ) {
				int ai = uniqList.get(i);
				
				if (dupMap.get(ai) > 1) {
					//duplicate itself
					continue;
				}
				
				int rootAi = ai / 2 + 1;
				
				boolean isOK = true;
				for(int j = 0 ; j < i ; j++ ) {
					int aj = uniqList.get(j);
					
					if ( ai % aj == 0 ) {
						isOK = false;
						break;
					}
					
					if ( aj > rootAi) {
						break;
					}
				}
				
				if ( isOK ) {
//					System.out.println(ai);
					ans++;
				}
			}
			
			System.out.println(ans);
			
		}
	}

}