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: Accepted)

import java.util.Arrays;
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[] A = new int[N];
            for (int i = 0; i < N; i++) {
                A[i] = sc.nextInt();
            }

            Arrays.sort(A);

            int count = 0;
            boolean[] used = new boolean[(int) (1e6 + 1)];
            for (int i = 0; i < N; i++) {
                if (i + 1 < N && A[i] == A[i + 1]) {
                } else if (i - 1 >= 0 && A[i] == A[i - 1]) {
                } else if (used[A[i]]) {
                } else {
                    count++;
                }
                if (!used[A[i]]) {
                    for (int j = A[i]; j < used.length; j += A[i]) {
                        used[j] = true;
                    }
                }
            }

            System.out.println(count);
        }
    }
}