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 JAVA (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Random;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int cnt = 0;
        for (int i = 0; i < n; i++){
            int m = Integer.parseInt(br.readLine());
            if (millerRabinTest(m)){
                cnt++;
            }
        }
        System.out.println(cnt);
    }
    public static int modPow(int a, int b, int d){
        String bit = Integer.toBinaryString(b);
        int ret = 1;
        for (int i=0; i<bit.length(); i++){
            ret *= ret;
            if (Integer.parseInt(""+bit.charAt(i))==1){
                ret *= a;
            }
            ret %= d;
            }
        return ret;
    }
    public static boolean millerRabinTest(int q){
        if (q == 2) return true;
        if (q < 2 || ((q & 1) == 0)) return false;

        int d = (q - 1) >> 1;
        while ((d & 1) == 0){
            d >>= 1;
        }
        
        int k = 50;
        Random r = new Random();
        for (int i = 0; i < k; i++){
            int a = 1 + r.nextInt(q-1);
            int t = d;
            int y = modPow(a, t, q);
            while (t != q - 1 && y != 1 && y != q - 1){
                y = modPow(y, 2, q);
                t <<= 1;
            }
            if (y != q - 1 &&(t&1) == 0){
                return false;
            }
        }
        return true;
    }
}