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: Memory Limit Exceeded)

from math import sqrt
n = int(input())
e = sorted([int(input()) for _ in range(n)])
L, pnum, tmp = sqrt(e[-1]+1), [], [i for i in range(2, e[-1]+1)]
while tmp[0] < L:
    v = tmp.pop(0)
    pnum.append(v)
    tmp = list(filter(lambda x: x%v!=0, tmp))
for t in tmp: pnum.append(t)
print(sum(1 for v in e if v in pnum))