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 Scala (2.11.7) (judge verdict: Wrong Answer)

object Main {
  def main(args: Array[String]): Unit = {
    val sc = new java.util.Scanner(System.in)
    val input = sc.nextInt()

    val result = nextPrime(input)

    println(result.toString)
  }

  @scala.annotation.tailrec
  def nextPrime(num: Int): Int = {
    val isPrime =
      (2.to(math.ceil(math.sqrt(num)).toInt)).forall(value => num % value != 0)
    if (isPrime) {
      num
    } else {
      nextPrime(num + 1)
    }
  }
}