usually, when it comes to some kind of computational geometry, I try to perform as many calculations as possible in integers, firstly they are faster, I'm not quite sure that I understand what is under the hood of real transformations, but there were many moments when I got TLE on them, I also find this option much more convenient, especially in this problem, where it is enough to square the remaining boundaries

FPE. Better to write like 15 more lines than to gamble AC by doing sqrt().