Problem:
Prime Numbers

A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.

Write a program which reads a list of N integers and prints the number of prime numbers in the list.

Input

The first line contains an integer N, the number of elements in the list.

N numbers are given in the following lines.

Output

Print the number of prime numbers in the given list.

Constraints

1 ≤ N ≤ 10000

2 ≤ an element of the list ≤ 108

Sample Input 1

5
2
3
4
5
6

Sample Output 1

3

Sample Input 2

11
7
8
9
10
11
12
13
14
15
16
17

Sample Output 2

4

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace Topic01
{
    class ALDS1_1_C
    {
        static void Main(string[] args)
        {
            int N = int.Parse(ReadLine());

            int[] M = new int[N];
            for (int i = 0; i < N; i++)
            {
                M[i] = int.Parse(ReadLine());
            }
            Array.Sort(M);
            ALDS1_1_C my = new ALDS1_1_C();
            bool[] IsPrime = my.GetPrimes(M.Last());

            int result = 0;
            for (int i = 0; i < N; i++)
            {
                if (IsPrime[M[i]]) result++;
            }

            WriteLine(result.ToString());
            ReadKey();
        }

        bool[] GetPrimes(int N)
        {
            bool[] IsPrime = new bool[N + 1];
            for (int i = 2; i <= N; i++)
            {
                IsPrime[i] = true;
            }

            for (int i = 2; i * i <= N; i++)
            {
                if (IsPrime[i])
                {
                    for (int j = 2 * i; j <= N; j += i)
                    {
                        IsPrime[j] = false;
                    }
                }
            }

            return IsPrime;
        }
    }
}