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 C# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Linq;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split()
                .Select(int.Parse).ToArray();

            Array.Sort(a);
            int result = 0;

            bool[] dp = new bool[a.Max() + 1];

            for (int i = 0; i < n; i++)
            {
                if (dp[a[i]])
                {
                    continue;
                }
                if(a[i] != a[i + 1])
                {
                    result++;
                }
                for (int j = a[i]; j <= a.Max(); j += a[i])
                {
                    dp[j] = true;
                }
            }
            if(!dp[a[n - 1]])
            {
                result++;
            }
            Console.WriteLine(result);
        }
    }
}