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 sosuu(int );
int main(){
  int i,j,n,key,c=0;
  int *a;
  
  scanf("%d",&n);

a=malloc(n*sizeof(int));

  for(i=0;i<n;i++){
    scanf("%d",&a[i]);
  }

  for(i=1;i<n;i++){
    key=a[i];
    j=i-1;
    while(j>=0 && a[j]>key){
      a[j+1]=a[j];
      j--;
    }
    a[j+1]=key;
  }
  c+=sosuu(a[0]);
  for(i=1;i<n;i++){
    if (a[i]!=a[i-1]){
     c += sosuu(a[i]); 
    }
  }
  printf("%d\n",c);
  return 0;
}

int sosuu(int x){
  int i,j=0;
  if(x==1)return 0;
  for(i=2; i <= x/2 ;i++){
    if(x%i==0)return 0;
  }
  return 1;
}