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>
#include<math.h>
#include <stdlib.h>
#define NMAX 100000000
void eratosthenes(int A[]);
int main(void){
    int n,i,x,cnt=0;
    unsigned int *A;
    A = (unsigned int *)malloc(sizeof(unsigned int) * NMAX);
    if (A == NULL) exit(0);
    eratosthenes(A);
    scanf("%d", &n);
    for(i=0;i<n;i++){
        scanf("%d", &x);
        if(x != 0 && A[x-1]){
            cnt++;
        }
    }
    printf("%d\n",cnt);

    free(A);

    return 0;
}

void eratosthenes(int A[]){
    int i,j;
    A[0] = 0;
    for(i=1;i<NMAX;i++){
        A[i]=1;
    }
    for(i=0;i<sqrt((double)NMAX);i++){
        if(A[i] == 1){
            for(j=(i+1)*2-1;j<NMAX;j+=(i+1)){
                A[j] = 0;
            }
        }
    }
}