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)

#[allow(unused_imports)]
use proconio::{fastout, input};

#[fastout]
fn main() {
    input!(x: usize);

    let mut bool_array = vec![true; 100005];
    let max_f = 100000.0_f64;

    for i in 2..max_f.sqrt().floor() as usize {
        if !bool_array[i] {
            continue;
        }
        for j in 0..100005 {
            if i == j {
                continue;
            }
            if j % i == 0 {
                bool_array[j] = false;
            }
        }
    }

    for i in x..100005 {
        if bool_array[i] {
            println!("{}", i);
            break;
        }
    }
}