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 C++ (judge verdict: Memory Limit Exceeded)

#include <iostream>
using namespace std;

const int LIM = 100000000;
bool notprime[LIM];

void take_prime(int num){
    notprime[0] = notprime[1] = true;
    int m = 2;
    while( m < 10000 ){
        if( !notprime[m] ){
            int j = m*m;
            while(j < LIM){
                notprime[j] = true;
                j += m;
            }
        }
        m++;
    }
    int cnt = 0;
    m = 2;
    while( cnt < num ){
        if( !notprime[m] ){
            cout << m << '\n';
            cnt++;
        }
        m++;
    }
}

int main(){
    int N;
    cin >> N;
    take_prime(N);
    return 0;
}