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)

def eratos(n):
	is_prime = [True for i in range(n+1)]
	is_prime[0] = False
	is_prime[1] = False
	for i in range(2, n):
		if i * i > n:
			break
		for j in range(i*i, n, i):
			is_prime[j] = False
	return is_prime

is_prime = eratos(10000)
primes = []
for i in range(10001):
    if is_prime[i] is True:
        primes.append(i)

n = int(input())
ans = 0
for _ in range(n):
    x = int(input())
    if x <= 10000:
        if is_prime[x] is True:
            ans += 1
    else:
        ok = True
        for i in primes:
            if i * i > x:
                break
            if x % i:
                ok = False
                break
        if ok is True:
            ans += 1
    
print(ans)