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>

int main()
{
  int n;   //numbers of input
  int inp[10000];   //input variable
  int i, j, count=0;   //loop counter variable
  int div;   //divisor

  scanf("%d", &n);
 
  //error processing
  if( 1 > n || n > 10000 ) printf("範囲外です。\n");
 
  else {
    //input of integers 
    for( i = 0 ; i < n ; i++ ) scanf("%d", &inp[i]);
    
    for( i = 0 ; i < n ; i++ ){
      if( 2 > inp[i] && inp[i] > 100000000 ) printf("範囲外です。\n");
      else{
	div = 0;
	for( j = 1 ; j <= inp[i] ; j++ ){
	  if( inp[i] % j == 0 ) div++;
	}
	//count the prime number
	    if( div == 2 ) count++;
      }
    }
    printf("%d\n", count);
  }

  return 0;
}