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 Python3 (judge verdict: Wrong Answer)

class PrimeChecker:

    def __init__(self):
        self.primes = [2,3]

    def isPrime(self, n):
        if n in self.primes:
            return True
        else:
            for i in self.primes:
                if n % i == 0:
                    return False

        i = 5
        w = 2

        while i * i < n:
            if n % i == 0:
                return False

            i += w
            w = 6 - w

        self.primes.append(n)

        return True

primeChecker = PrimeChecker()
count = 0
N = int(input())
for _ in range(N):
    if primeChecker.isPrime((int(input()))):
        count += 1
print(count)