Aizu - ALDS1_1_C Prime Numbers(数论-质数检验)

Description

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 Input1

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

---

#include <iostream>
#include <vector>
#include <cmath>
#include <string>
#include <climits>
#include <cstdio>
#include <queue>
#include <stack>
#include <map>
#include <algorithm>

using namespace std;

bool isPrime(int n)
{
    if (n == 2) return true;
    if (!(n & 1)) return false;
    int limit = sqrt(n) + 1;
    for (int i = 3; i <= limit; i += 2) {
        if (n % i == 0) return false;
    }

    return true;
}

int main()
{
    std::ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);

    int caseNum;
    cin >> caseNum;

    int cnt = 0;
    while (caseNum--) {
        int n;
        cin >> n;
        if (isPrime(n)) ++cnt;
    }
    cout << cnt << endl;

    return 0;
}