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 Rust (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::iter::*;
#[allow(unused_imports)]
use std::cmp::*;

struct Scanner<R: Read> {
    reader: R,
}

#[allow(dead_code)]
impl<R: Read> Scanner<R> {
    fn new(reader: R) -> Scanner<R> {
        Scanner { reader: reader }
    }

    fn safe_read<T: FromStr>(&mut self) -> Option<T> {
        let token = self.reader.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        if token.is_empty() {
            None
        } else {
            token.parse::<T>().ok()
        }
    }

    fn read<T: FromStr>(&mut self) -> T {
        if let Some(s) = self.safe_read() {
            s
        } else {
            writeln!(std::io::stderr(), "Terminated with EOF").unwrap();
            std::process::exit(0);
        }
    }

    fn vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
        (0..len).map(|_| self.read()).collect()
    }

    fn mat<T: FromStr>(&mut self, row: usize, col: usize) -> Vec<Vec<T>> {
        (0..row).map(|_| self.vec(col)).collect()
    }
}

fn main() {
    std::thread::Builder::new()
        .stack_size(104_857_600)
        .spawn(solve)
        .unwrap()
        .join()
        .unwrap();
}

fn is_prime(n: u32) -> bool {
    if n <= 1 {
        return false;
    }
    for i in 2..n {
        if i * i > n {
            break;
        }
        if n % i == 0 {
            return false;
        }
    }
    true
}

fn eratosthenes_sieve(n: usize) -> Vec<bool> {
    let mut is_prime = vec![true; n + 1];
    is_prime[0] = false;
    is_prime[1] = false;
    for i in 2..n+1 {
        if is_prime[i] {
            let mut j = i * i;
            while j <= n {
                is_prime[j] = false;
                j += i;
            }
        }
    }
    is_prime
}

fn solve() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);

    let n = sc.read();
    let is_prime = eratosthenes_sieve(100000000);
    let mut cnt = 0;
    for _ in 0..n {
        let x: usize = sc.read();
        if is_prime[x] {
            cnt += 1;
        }
    }
    println!("{}", cnt);
}