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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ProconTemplate
{
    //https://atcoder.jp/contests/abc141/tasks/abc141_c
    class abc169_b
    {
        //private static int[] m_aiPrimes;
        //private static int m_iCurPrimeIdx;
        public static void Main(string[] args)
        {
            //int N = int.Parse(Console.ReadLine());

            //string s = Console.ReadLine();
            //int[] xi = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

            //string[] asInput = Console.ReadLine().Split(' ');
            //int X = int.Parse(asInput[0]);
            //int N = int.Parse(asInput[1]);

            //long A = long.Parse(asInput[0]);
            //decimal B = decimal.Parse(asInput[1]);
            //Console.WriteLine(A * (long)(100 * B) / 100);

            int N = int.Parse(Console.ReadLine());
            int[] xi = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

            Array.Sort(xi);
            int iAns = 0;

            for (int i = 0; i < N; i++)
            {
                bool bFlg = false;
                for (int j = 0; j < i; j++)
                {
                    if (xi[i] % xi[j] == 0)
                    {
                        bFlg = true;
                        break;
                    }
                }
                if (bFlg == false)
                {
                    if (i == N - 1 || xi[i+1] != xi[i] )
                    {
                        iAns++;
                    }
                }
            }

            Console.WriteLine(iAns);
        }

    }
}