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>

void make_prime();

int max=100000000;
int prime[100000010];

int main()
{
	int n,i,x;
	int count=0;
	make_prime();
	scanf("%d", &n);
	for(i=0; i<n; i++){
		scanf("%d", &x);
		if(prime[x]){
			count++;
		}
	}
	printf("%d\n", count);
	return 0;
}

void make_prime()
{
	int i,k;
	for(i=0; i<=max; i++){
		prime[i]=1;
	}
	prime[0]=0;
	prime[1]=0;
	for(i=2; i<=max; i++){
		if(prime[i]){
			for(k=i+i; k<=max; k+=i){
				prime[k]=0;
			}
		}
	}
	return;
}