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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun is-prime(x i)
  (if (= x 1)
	nil
	(if (= x 2)
	  t
	  (if (zerop (mod x i))
		nil
		(if (<= (* i i) x)
		  (is-prime x (1+ i))
		  t)))))

(defun func(x)
  (if (is-prime x 2)
	x
	(func (1+ x))))

(let ((x (read)))
  (princ (func x)))