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.Collections.Generic;
using System.Linq;

namespace AtCoder200531
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            List<int> inputs = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToList();

            inputs.Sort();

            int count = n;
            for (int j = 0; j < n; j++)
            {
                for (int i = n-1; i > j; i--)
                {
                    if (inputs[i] % inputs[j] == 0)
                    {
                        count--;
                        break;
                    }
                }
            }
            if (inputs[0] == inputs[1])
            {
                count--;
            }

            Console.WriteLine(count);
        }
    }
}