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 C (judge verdict: Time Limit Exceeded)

#include <stdio.h>

int prime_check(long num) {
    int i, n;
    long max;

    if (num%2==0) {
        max=num/2;
    } else {
        max=num/2+1;
    }
    n=0;
    for (i=1;i<=max;i++) {
        if (num%i==0) n++;
        if (i!=(num-i)) {
            if (num%(num+1-i)==0) n++;
        }
    }
    if (num==2) n=2;
    if (n==2) return 1;
    return 0;
}

int main(void) {
    int i, n, boo, count;
    long num;

    scanf("%d", &n);
    count=0;
    for (i=0; i<n; i++) {
        scanf("%ld", &num);
        boo=prime_check(num);
        if (boo==1) count++;
    }
    printf("%d\n", count);
    return 0;
}