CF1936F.Grand Finale: Circles

The 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.

Output three real values, $x$ , $y$ , and $r$ — the coordinates of the center and the radius of the circle.

A 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.

A 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.