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::input;

fn sieve(n: usize) -> (Vec<usize>, Vec<bool>) {
  let mut primes = Vec::new();
  let mut is_prime = vec![true; n];
  is_prime[0] = false;
  is_prime[1] = false;
  for i in 2..n { 
    if is_prime[i] {
      primes.push(i);
    }
    for &p in &primes {
      if i * p >= n {
        break;
      }
      is_prime[i * p] = false;
      if i % p == 0 {
        break;
      }
    }
  }
  (primes, is_prime)
}

fn main() {
  input! { 
    x: usize,
  }
  let (_, is_prime) = sieve(2*x);
  for p in x..2*x {
    if is_prime[p] {
      println!("{}", p);
      break;
    }
  }
}