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: Memory Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Text;

class Program
{
    public void Proc()
    {
        int itemCount = int.Parse(Console.ReadLine());
        List<int> numList = new List<int>();
        for(int i=0; i<itemCount; i++)
        {
            int num = int.Parse(Console.ReadLine());
            numList.Add(num);
        }
        numList.Sort();
        Dictionary<int, bool> sosu = GetSosuList(numList[numList.Count - 1]);
        int sosuCount = 0;
        foreach(int num in numList)
        {
            if(sosu.ContainsKey(num))
            {
                sosuCount++;
            }
        }
        Console.WriteLine(sosuCount);
    }

    private Dictionary<int, bool> GetSosuList(int max)
    {
        Dictionary<int, bool> dic = new Dictionary<int, bool>();
        Dictionary<int, bool> sosu = new Dictionary<int, bool>(); 
        for(int i=2; i<=max; i++)
        {
            if(!dic.ContainsKey(i))
            {
                sosu.Add(i, true);
                dic.Add(i, true);
            }
            int num = i;
            int mul = 2;
            while(num * mul <= max)
            {
                int result = num * mul;
                if(!dic.ContainsKey(result))
                {
                    dic.Add(num * mul, false);
                }
                mul++;
            }
        }
        return sosu;
    }

    static void Main(string[] args)

    {

        Program prg = new Program();
        prg.Proc();

    }
}