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 (1.15.1) (judge verdict: Accepted)

fn main() {
	let mut s = String::new();
	std::io::stdin().read_line(&mut s).unwrap();
	let x: u32 = s.trim().parse().unwrap();
	let mut sieve = vec![true; 100003 + 1];
	sieve[0] = false;
	sieve[1] = false;
	for i in (2..).take_while(|i| i * i < 100004) {
		if sieve[i] {
			for j in (2..).map(|j| j * i).take_while(|j| *j < 100004) {
				sieve[j] = false;
			}
		}
	}
	for x in x as usize.. {
		if sieve[x] {
			println!("{}", x);
			break;
		}
	}
}