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.util.*;

public class Main {
	public static boolean is_prime(int x){
		for(int e = 2 ; e <= Math.sqrt(x) ; e++){
			if(x % e ==0) return false;
		}
		return true;
	}
	public static void main(String[] args) {
		int c = 0;
		Scanner scn = new Scanner(System.in);
		int N = scn.nextInt();
		boolean[] tof = new boolean[100000000];
		Arrays.fill(tof, false);
		for(int i = 1 ; i <= N ; i++){
			int k = scn.nextInt();
			if(tof[k-1] == false){
				if(is_prime(k)) tof[k] = true;
			}
		}
		for(int j = 0 ; j < 100000000 ; j++){
			if(tof[j] == true) c++;
		}
		System.out.println(c);
	}

}