Problem:
Score: 300 points

Problem Statement

Find the minimum prime number greater than or equal to X.

Notes

A prime number is an integer greater than 1 that cannot be evenly divided by any positive integer except 1 and itself.

For example, 2, 3, and 5 are prime numbers, while 4 and 6 are not.

Constraints

2 \le X \le 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X

Output

Print the minimum prime number greater than or equal to X.

Sample Input 1

20

Sample Output 1

23

The minimum prime number greater than or equal to 20 is 23.

Sample Input 2

2

Sample Output 2

2

X itself can be a prime number.

Sample Input 3

99992

Sample Output 3

100003

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::{fastout, input};
#[allow(unused_mut)]
#[fastout]
fn main() {
    input! {
        x: usize
    }
    for i in x..=100003usize {
        if i.is_prime() {
            println!("{}", i);
            return;
        }
    }
}

trait Prime {
    fn is_prime(&self) -> bool;
}

impl Prime for usize {
    fn is_prime(&self) -> bool {
        let n = *self;
        if n <= 1 {
            return false;
        }

        if n == 2 {
            return true;
        }
        let lim = (n as f64).sqrt().ceil() as usize;
        for i in 2..=lim {
            if n % i == 0 {
                return false;
            }
        }
        true
    }
}