for each test case, there are a number of points (hundreds, thousands) on a 2d plane. it's easy to draw a square to contain all of them. minimize such square's sidelength. the smallest square can touch the points but there cannot be points outside of it. the error tolerance can be 1e-4.

i have competed in icpc and got mediocre rankings and have solved over a thousand algorithm puzzles (kattis, project euler, leetcode, hacker rank, etc.) so this is not going to be too esoteric, i hope. i thought of this question watching youtuber mathloger.

if you know the solution please don't say it.