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.util.*;

/**
 * C
 */
public class Main {
    public static void main(String[] args) {
        
        int prime = 0;
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int array[] = new int[n];

        for(int i=0; i<n; i++) {
            array[i] = sc.nextInt();
        }

        sc.close();

        for(int num : array) {
            if(isPrime(num) == true) {
                prime++;
            }
        }

        /*IN : for (int num : array) {
            for (int j = 2; j<num; j++) {
                if (num % j == 0) {
                    continue IN;
                }
            }
            prime++;
        }
        
        これでだめだったから悲しいよなぁ。。。
        巨大な数が来た時に計算速度がバカ落ちる。

        */

        System.out.println(prime);

    }


    // 判定メソッドを作ったほうがいい
    public static boolean isPrime(int num) {

        if (num < 2) {
            return false;
        } else if (num == 2) {
            return true;
        } else if (num % 2 == 0) {
            return false; // 偶数はあらかじめ除く
        }

        double sqrtNum = Math.sqrt(num);
        for (int i = 3; i <= sqrtNum; i += 2) {
            if (num % i == 0) {
                // 素数ではない
                return false;
            }
        }

        // 素数である
        return true;
    }
}