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 2.0.3) (judge verdict: Accepted)

(let* ((x (read))
       (y (make-array `(,(1+ (* 2 x))) :initial-element t)))
  (loop :for i :from 2 :to (ceiling (sqrt (* 2 x)))
        :if (aref y i)
        :do (loop :for j :from (* i 2) :to (* 2 x) :by i
                  :do (setf (aref y j) nil)))
  (loop :for i :from x :to (* 2 x)
        :if (aref y i)
        :return (format t "~A~%" i)))