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 LIB;
using System;
using System.Linq;
using System.Text;
using System.Collections.Generic;

class Program
{
    public static IO IO = new IO();
    static void Main(string[] args)
    {
        int n = IO.INT();
        int[] m = IO.INT(n);
        int p = 0;
        for (int i = 0; i < n; i++)
        {
            if (m[i] == 2) { p++; }
            else if (m[i] > 2 && (m[i] % 2 != 0))
            {
                bool f = true;
                int q = (int)Math.Sqrt(m[i]);
                for (int j = 3; j < q; j += 2) { if (m[i] % j == 0) { f = false; break; } }
                if (f) { p++; }
            }
        }
        IO.WRITE(p);
        IO.FLUSH();
    }
}

namespace LIB
{
    public class IO
    {
        private const int WMAX = 1000;
        private StringBuilder S = new StringBuilder();
        private T R<T>(Func<string, T> f) { return f(Console.ReadLine()); }
        private T[] R<T>(Func<string, T> f, char c) { return STRING().Split(c).Select(f).ToArray(); }
        private T[] R<T>(Func<string, T> f, int l) { T[] r = new T[l]; for (int i = 0; i < l; i++) { r[i] = R(f); } return r; }
        private T[][] R<T>(Func<string, T> f, int l, char c) { T[][] r = new T[l][]; for (int i = 0; i < l; i++) { r[i] = R<T>(f, c); } return r; }
        private void W<T>(Func<T, string> f, T v, bool lf = true) { S.Append(f(v)); if (lf == true) { S.Append('\n'); } if (S.Length >= WMAX) { FLUSH(); } }
        public string STRING() { return R(s => s); }
        public string[] STRING(char c) { return R(s => s, c); }
        public string[] STRING(int l) { return R(s => s, l); }
        public string[][] STRING(int l, char c) { return R(s => s, l, c); }
        public int INT() { return R(int.Parse); }
        public int[] INT(char c) { return R(int.Parse, c); }
        public int[] INT(int l) { return R(int.Parse, l); }
        public int[][] INT(int l, char c) { return R(int.Parse, l, c); }
        public long LONG() { return R(long.Parse); }
        public long[] LONG(char c) { return R(long.Parse, c); }
        public long[] LONG(int l) { return R(long.Parse, l); }
        public long[][] LONG(int l, char c) { return R(long.Parse, l, c); }
        public double DOUBLE() { return R(double.Parse); }
        public double[] DOUBLE(char c) { return R(double.Parse, c); }
        public double[] DOUBLE(int l) { return R(double.Parse, l); }
        public double[][] DOUBLE(int l, char c) { return R(double.Parse, l, c); }
        public void WRITE(string s, bool lf = true) { W(v => v, s, lf); }
        public void WRITE(int s, bool lf = true) { W(v => v.ToString(), s, lf); }
        public void WRITE(long s, bool lf = true) { W(v => v.ToString(), s, lf); }
        public void WRITE(double s, bool lf = true) { W(v => v.ToString(), s, lf); }
        public void FLUSH() { Console.Write(S); S.Length = 0; }
    }
}