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 <iostream>
#include <algorithm>
#include <vector>
#include <stack>
#include <queue>
#include <map>
#include <cmath>
#include <string>
#include <sstream>
#include <iomanip>
#include <complex>
using namespace std;

#define ll long long
#define vvi vector< vector<int> >
#define vi vector<int>
#define All(X) X.begin(),X.end()
#define FOR(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define pb push_back
#define pii pair<int,int>
#define mp make_pair
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}

#define intmax 100000003
bool isprime[intmax];
void makeprime(int datasize){/*??¨???????????????????????????*/
	REP(i,datasize) if(i%2!=0) isprime[i] = true;
	isprime[1] = false;
	isprime[2] = true;
	for(ll int i=3;i<sqrt(datasize);i+=2){
		for(ll int j=i+2;j<datasize;j+=2){
			if(j%i==0) isprime[j] = false;
		}
	}
}

int main(){
	int n;
	cin >> n;
	int cnt = 0;
	ll int mmax = -1;
	ll int data[10001];
	REP(i,n){
		ll int tmp;
		cin >> tmp;
		data[i] = tmp;
		mmax = max(mmax,tmp);
	}
	makeprime(mmax+1);
	REP(i,n){
		if(isprime[data[i]]) cnt++;
	}
	cout << cnt << endl;
}