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: Accepted)

import math

n = int(input())
a = sorted([int(input()) for i in range(n)])
max_sqrt = int(math.sqrt(a[-1]))
screen = list(range(2, max_sqrt+1))
index = 0

while index < len(screen):
    screen = screen[:index+1] + list(filter(lambda x: x % screen[index] != 0, screen[index+1:]))
    index += 1

b = []
for i in range(len(a)):
    is_prime = True
    for j in range(len(screen)):
        if a[i] != screen[j] and a[i] % screen[j] == 0:
            is_prime = False
            break
    if is_prime:
        b.append(a[i])

print(len(b))