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 helper(v: usize) -> bool {
  if v <= 1 {
    return false
  }

  if v == 2 {
    return true
  }

  if v % 2 == 0 {
    return false
  }
  
  let mut index = 3;
  while index < v {
    if v % index == 0 {
      return false
    }
    index += 2;
  }

  true
}

fn main() {
  input! {
    x: usize
  }
  let max = 10usize.pow(5) + 10;
  
  for i in x..=max {
    if helper(i) {
      println!("{}", i);
      return
    }
  }
}