F. Grand Finale: Circlestime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given n circles on the plane. The i-th of these circles is given by a tuple of integers (x_i, y_i, r_i), where (x_i, y_i) are the coordinates of its center, and r_i is the radius of the circle.Please find a circle C which meets the following conditions:  C is contained inside all n circles given in the input.  Among all circles C that meet the first condition, the radius of the circle is maximum. Let the largest suitable circle have the radius of a.Your output C, described as (x,y,r), will be accepted if it meets the following conditions:  For each i, \sqrt{(x_i-x)^2+(y_i-y)^2}+ r \le r_i+\max(a,1)\cdot 10^{-7}.  The absolute or relative error of r does not exceed 10^{-7}. Formally, your answer is accepted if and only if \frac{\left|r - a\right|}{\max(1, a)} \le 10^{-7}. InputThe first line contains a single integer n (1 \le n \le 10^5) — the number of circles.The i-th of the following n lines contains three integers x_i, y_i, r_i (-10^6 \le x_i,y_i \le 10^6, 1 \le r_i \le 2 \cdot 10^6).It is guaranteed that there is a circle with a radius of at least 10^{-6} which is contained inside all n circles.OutputOutput three real values, x, y, and r — the coordinates of the center and the radius of the circle.ExamplesInput
4
1 1 3
-1 1 3
1 -1 2
-1 -1 2
Output
0.0000000000000000 -0.7637626158259733 0.9724747683480533
Input
4
41580 -23621 95642
-41580 -23621 95642
0 47821 95642
0 0 109750
Output
0.0000000000000000 0.0000000000000000 47821.0000000000000000
NoteA two-dimensional plot depicting the first test case is given below. The output circle C is dashed with blue lines.  A two-dimensional plot depicting the second test case is given below. The output circle C is dashed with blue lines.  
4
1 1 3
-1 1 3
1 -1 2
-1 -1 2

0.0000000000000000 -0.7637626158259733 0.9724747683480533 
['binary search', 'geometry', '*3300']