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: Time Limit Exceeded)

using System;
using System.Linq;

namespace AtCoder.Abc
{
    class QuestionD
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var n = int.Parse(Console.ReadLine());
            var sp = Console.ReadLine().Split(' ');
            var a = sp.Select(i => int.Parse(i)).ToArray();
            var w = new int[1000000];

            var cnt = 0;
            for (var i = 0; i < n; i++)
            {
                if (w[a[i]-1] == -1) continue;
                var f = true;
                for (var j = 0; j < n; j++)
                {
                    if (i == j) continue;
                    if (a[i] % a[j] == 0)
                    {
                        w[a[i] - 1] = -1;
                        f = false;
                        break;
                    }
                }
                if (f)
                {
                    cnt++;
                }
            }
            Console.WriteLine(cnt);

            Console.Out.Flush();
        }
    }
}