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# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

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

namespace D
{
    class Program
    {
        static int MAXArray = 50000000;
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var A = new int[N];
            var inputA = Console.ReadLine().Split(' ');
            for (int i = 0; i < N; i++)
            {
                A[i] = int.Parse(inputA[i]);
            }

            var divisor = new int[MAXArray];
            var undivisibleCount = 0;
            for (int i = 0; i < N; i++)
            {
                for (int j = 1; j < divisor.Length/A[i]; j++)
                {
                    divisor[A[i] * j]++;
                }
            }
            for (int i = 0; i < N; i++)
            {
                if (divisor[A[i]] == 1)
                {
                    undivisibleCount++;
                }
            }

            Console.WriteLine(undivisibleCount);
        }
    }
}