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: Memory Limit Exceeded)

#include <stdio.h>

#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define REP(i, n) FOR(i,0,n)

#define size (int)1e8+5
int isPrime[size];

void solver() {
    isPrime[0] = isPrime[1] = 0;
    for (int i = 2; i < size; ++i) {
        isPrime[i] = 1;
    }
    for (int i = 2; i < size; ++i) {
        if (isPrime[i] == 1) {
            for (int j = 2 * i; j < size; j += i) {
                isPrime[j] = 0;
            }
        }
    }

    int N;
    int tmp;
    int sum = 0;

    scanf("%d", &N);
    for (int i = 0; i < N; ++i) {
        scanf("%d", &tmp);
        if (isPrime[tmp] == 1) {
            sum++;;
        }
    }

    printf("%d\n", sum);
}


int main() {
    solver();
    return 0;
}