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;

namespace ALDS1_1_C
{
    class Program
    {
        static List<int> primes = new List<int>();
        static int tmpMax = 1;
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            primes.Add(2);
            tmpMax = 2;
            int cnt = 0;
            while (n-- != 0)
            {
                var x = int.Parse(Console.ReadLine());
                if (x < tmpMax)
                {
                    if (primes.Contains(x)) cnt++;
                    else continue;
                } 
                var sqrt = (int)Math.Sqrt(x);
                bool isPrime = true;
                foreach (var p in primes)
                {
                    if (p > sqrt) break;
                    if (x % p == 0)
                    {
                        isPrime = false;
                        break;
                    }
                }
                for(int i=primes[primes.Count-1]+1;i<=sqrt; i++)
                {
                    if(x % i == 0)
                    {
                        isPrime = false;
                        break;
                    }
                }
                if (isPrime) cnt++;
            }
            Console.WriteLine(cnt);
        }
    }
}