The Ice-Cool Princess Claims Me (GL)

What the heck? One moment she was washing up at home, and the next she was staring down a roomful of ancient people in an old-fashioned room. Then a System appeared and ordered her to go to the capital and pick up a rich guy. But where was the rich guy? Why the hell had it given her a girl instead!? An icy ancient princess top x a seemingly sweet, modern-day genius student bottom