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++11 (judge verdict: Accepted)

#include <algorithm>
#include <bitset>
#include <cctype>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using namespace std;

const int MAX_NUM = 100000000;
vector<bool> ps(MAX_NUM + 1, true);

int main() {
    ps[0] = ps[1] = false;
    for (int i = 4; i <= MAX_NUM; i += 2) {
        ps[i] = false;
    }
    for (int i = 3; i + i <= MAX_NUM; i += 2) {
        if (!ps[i]) {
            continue;
        }
        for (int j = i + i; j <= MAX_NUM; j += i) {
            ps[j] = false;
        }
    }

    int n;
    cin >> n;
    int ans = 0;
    for (int i = 0; i < n; i++) {
        int k;
        cin >> k;
        if (ps[k]) {
            ans++;
        }
    }
    cout << ans << endl;
}