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 Python (judge verdict: Time Limit Exceeded)

import functools
def divise(n, divisor):
    if n % divisor == 0 and n != divisor:
        return 0
    else:
        return n

if __name__ == '__main__':
    number = input()
    origin = [int(input()) for _ in range(number)]

    divised = origin

    hoge = []
    for i in range(number):
        hoge.append(True)

    for i in range(2, max(origin)+1):
        divised = list(map(functools.partial(divise, divisor=i), divised))

    for j in range(number):
        if divised[j] == 0:
            hoge[j] = False

    cnt = 0
    for b in hoge:
        if b:
            cnt += 1
    print(cnt)