Alyssa, Bilal, Constantine, and Daiyu each live in a house that is numbered with a positive integer.
A four-digit perfect square is formed by writing Alyssa’s house number followed by Bilal’s house number. Another four-digit perfect square is formed by writing Constantine’s house number followed Daiyu’s house number. Constantine’s house number is \(31\) more than Alyssa’s house number, and Daiyu’s house number is \(31\) more than Bilal’s house number. What is each person’s house number?