9154: Geometry Problem

You are given $n$ $\text{distinct}$ circles in the 2-dimensional plane. Please find a minimum square to enclose all the circles.

The first line contains a single integer $n$ (1≤n≤5×104)(1\le n\le 5\times 10^4)(1≤n≤5×104), denoting the number of circles.
Then follows $n$ lines, each line contains three integers x, y, rx,~y,~rx, y, r (−106≤x,y≤106, 1≤r≤106)(-10^6 \le x,y\le 10^6,~ 1\le r\le 10^6)(−106≤x,y≤106, 1≤r≤106), denoting a circle with its center at (x,y)(x,y)(x,y) and radius $r$.

Print a single real number - the minimum side length of the square. Your answer will be accepted if the absolute or relative error to the jury's answer is less than or equal to 10−610^{-6}10−6.

4
0 100 50
100 0 50
-100 0 50
0 -100 150

341.4213562373

The first example is shown as follows: