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.Scanner;
import java.util.Arrays;

public class Main { 
  public static void main(String[] args) {
    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);
    boolean[] dp = new boolean[1000001];
    int count =0;
    for (int i =0; i<N; i++) {
      dp[A[i]] = true;
    }
    for (int i =0; i<N; i++) {
      int j = A[i] * 2;
      while (j < 1000001) {
        dp[j] = false;
        j+= A[i];
      }
    }
    for (int i =0; i<N; i++) {
      if (i <N-1 && A[i] == A[i+1]) {
        dp[A[i]] = false;
      }
      if (dp[A[i]] == true) {
        count++;
      }
    }
    System.out.println(count);
  }
}