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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program main
      implicit none
      integer :: x
      integer :: i, j
      logical :: flag

      read *, x
      do i = x, 100003
        flag = .true.
        do j = 2, int(sqrt(real(x))+1)
          if ( mod(i,j) == 0 ) then
            flag = .false.
            exit
          end if
        end do
        if ( flag ) then
          print *, i
          stop
        end if
      end do

end program main