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 ABC149C
    implicit none
    integer(8)::X,i,j,div_max,flg
    read(5,*)X

    if(X==2)then
        print'(i0)',2
    else
        do i=X,100003
            div_max=int(sqrt(real(i)))+1
            flg=0
            do j=2,div_max
                if(mod(i,j)==0)then
                    flg=1
                    exit
                end if
            end do

            if(flg==0)then
                print'(i0)',i
                exit
            end if
        end do
    end if

end program ABC149C