Editorial for Another Contest 4 Problem 11 - Three Rectangles

Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.

The function to implement is to return true iff $n$ ~n~ can be written as the sum of three squares, as motivated by the problem statement and problem title.