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: Accepted)

import java.io.*;
import java.util.*;

class JudgingMchine {
    static boolean isPrime(int x) {
        if(x == 2) {
        return true;
    }
    if(x < 2 || x % 2 == 0) {
        return false;
    }

    int i =3;
    while(i <= Math.sqrt(x)) {
        if(x % i == 0) {
            return false;
        }
        i += 2;
    }
    return true;
    }
}

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

    List<Integer> nums = new ArrayList<>();
    for(int i=0; i<n; ++i) {
        nums.add(sc.nextInt());
    }

    int count = 0;
    for(int num : nums) {
        if(JudgingMchine.isPrime(num)) {
            count++;
        }
    }

    System.out.println(count);

    }
}