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: Accepted)

PROGRAM main
	implicit none
	integer :: x,xmax, xx
	read *, x
    xmax = 100000000
    do xx = x, xmax
      if (isPrimeNum(xx))then
      	print "(i0)", xx
        exit
       endif
    enddo
contains

	logical pure function isPrimeNum(n)
    	integer, intent (in) :: n
        integer :: i, iend
        
        iend = sqrt(dble(n))+1
        if(iend == n) iend = iend-1
    	isPrimeNum = .false.
        do i = 2 , iend
        	if (mod(n,i)==0) return
        enddo
        
	    isPrimeNum = .true.
    end function isPrimeNum

END PROGRAM main