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>
#include <stdlib.h>

int main() {

  int *p;
  int i,j;
  int n;
  int count = 0;
  
  scanf("%d",&n);
  
  p = (int *)malloc(n * sizeof(int)); //メモリ領域の確保

  for (i=0; i<n; i++)
    scanf("%d", &p[i]);
  if(n>10000 || n<1) return 0;
  
  /* 素数の判定 */
  for(i=0; i<n; i++) {
    for(j=2; j<p[i]+1; j++){
      if(p[i] == 2 || j == p[i]){ //2または最後まで割り切れなかった場合
	count++;
	break;
      }
      else if(p[i]%2 == 0) break; //偶数除外
      else if(p[i] % j == 0) break;
      else continue;
    }
  }

  printf("%d\n",count);
  
  return 0;
}