How did Noah managed to fit millions and millions of species on a single boat?

Noah's ark was only 450 feet long, 75 feet wide and 45 feet high. Besides the staggering number of species (alive or extinct today), how did he manage to cramped the dinosaurs and giant prehistoric mammals. Even if those animals were babies the sheer number of animals would require many square miles of space. I am starting to think that God gave Noah a shrink gun solve the problem.