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: Memory Limit Exceeded)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (Scanner in = new Scanner(System.in)) {
            int N = in.nextInt();
            int[] FURUI = new int[100_000_000 + 1];
            for (int i = 2; i < FURUI.length; i++) {
                FURUI[i] = 1;
            }
            for (int i = 2; i * i <= FURUI.length; i++) {
                if (FURUI[i] == 0) {
                    continue;
                }
                for (int j = i + i; j < FURUI.length; j += i) {
                    FURUI[j] = 0;
                }
            }
            int count = 0;
            while (N-- > 0) {
                count += FURUI[in.nextInt()];
            }
            System.out.println(count);
        }
    }
}