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 ABC149C
    implicit none
    real::n
    integer::i,Flag
    read*,n
    Flag = 1
    if(n==2) then
        print*,int(n)
        stop
    end if
    if (mod(int(n),2) == 0) then
        n = n + 1
    end if
    do
        Flag = 1
        if (n <= 10) then
            do i = 3,int(n)
                if (mod(int(n),i) == 0) then
                    Flag = 0
                end if
            end do
        else
            do i = 3,int(sqrt(n)),2
                if (mod(int(n),i) == 0) then
                    Flag = 0
                end if
            end do
        end if
        if (Flag == 1) then
            print*,int(n)
            stop
        else
            n = n + 1
        end if
    end do
end program ABC149C