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.Scanner;
 
class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		int max = 100000001;
		boolean [] sosuu = new boolean [max];
 		
		sosuulist(sosuu, max);
 		
 		syuturyoku(sosuu);
	}
 
	private static void sosuulist(boolean [] sosuu, int max) {
		for (int i = 1; i <= max - 1; i++) {
			sosuu[i] = true;
		}
		sosuu[0] = false;
		sosuu[1] = false;
 
		for (int i = 2; i <= Math.sqrt(max); i++) {
			if (sosuu[i] == true) {
				for (int j = i + i; j <= max - 1; j += i) {
					sosuu[j] = false;
				}
			}
		}
	}
	
	private static void syuturyoku(boolean [] sosuu) {
		int [] n = new int [10000];
		int count = 0;
		
		Scanner cin = new Scanner (System.in);
		int x = cin.nextInt();
 
		for (int i = 0; i < x; i++) {
			n[i] = cin.nextInt();
			if (sosuu[n[i]] == true) count++;
		}
 
		System.out.println(count);
	}
}