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: Wrong Answer)

using System;
using static System.Console;

namespace AOJ
{
    public class ALDS1_1_C
    {
        public static void Main(string[] args)
        {
            int N = int.Parse(ReadLine());
            var A = new int[N];
            for (int i = 0; i < N; i++)
            {
                A[i] = int.Parse(ReadLine());
            }

            int cnt = 0;
            for (int i = 0; i < N; i++)
            {
                if (IsPrimeB(A[i]))
                {
                    cnt++;
                }
            }
            
            WriteLine(cnt);
        }

        public static bool IsPrimeA(int x)
        {
            if (x <= 1) return false;

            int y = x - 1;
            while(y > 1)
            {
                if (x % y == 0) return false;
                y--;
            }

            return true;
        }

        public static bool IsPrimeB(int x)
        {
            if (x <= 1) return false;
            
            // Composite Number ==  not Prime Number
            bool isCompositeNumber = false; 
            
            double r = Math.Sqrt(x);
            
            for (int i = 2; i < r; i++)
            {
                if (x % i == 0) isCompositeNumber = true;
            }

            return !isCompositeNumber;
        }
    }
}