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: Accepted)

#include <stdio.h>

#define MAX 100000007

static unsigned char is_not_prime[((MAX + 1) + 7) / 8];

static inline int get_bit(int i) {
	return (is_not_prime[i >> 3] >> (i & 7)) & 1;
}

static inline void set_bit(int i) {
	is_not_prime[i >> 3] |= (1 << (i & 7));
}

void init(void) {
	int i, j;
	set_bit(0);
	set_bit(1);
	for (j = 4; j <= MAX; j += 2) set_bit(j);
	for (i = 3; i * i <= MAX; i += 2) {
		if (!get_bit(i)) {
			for (j = i * i; j <= MAX; j += i) set_bit(j);
		}
	}
}

int main(void) {
	int N, i;
	int count = 0;
	init();
	if (scanf("%d", &N) != 1) return 1;
	for (i = 0; i < N; i++) {
		int q;
		if (scanf("%d", &q) != 1) return 1;
		if (!get_bit(q)) count++;
	}
	printf("%d\n", count);
	return 0;
}