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: Runtime Error)

#include <stdio.h>

#define LIM	10000000
int arr[LIM];
int main(void) {
	int max = 2, i, j, k, n, num, cnt = 0;
	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		scanf("%d", &num);
		if (max < num) {
			for (j = max; j < num; j++) {
				if (arr[j]) continue;
				for (k = j * 2; k < LIM; k += j) {
					arr[k] = 1;
				}
			}
			max = num;
		}
		if (!arr[num]) cnt++;
	}
	printf("%d\n", cnt);
}