Part 1- Doctor Who?

One day, as Alice and Jefferson Hatter were walking into the room of doors; they are greeted with an odd blue box that was never there before. Upon further inspection, and a simple knock at the door the two love birds are face to face with two new faces emerging from the box. The Doctor and Clara is what they call themselves. What do you get when you put two madmen in a blue box that's bigger on the inside with two other madmen that has a top hat that's bigger on the inside? Well, I don't know so let's find out together!