Hadron Colliders#600
Two countries, Bytelandia and Flatlandia, have joined efforts in high-energy physics research and have built hadron colliders. Each collider is circular and located underground, and its thickness is negligible – we treat each collider as a circle.
The first line of the input contains an integer (1 \leq n \leq 3). Each of the following lines describes one collider. The -th collider is specified by three integers , , – the coordinates of its center and its radius (|x|, |y| \leq 1000, 1 \leq r \leq 1000). Colliders do not have common points, none is inside another, and if n=3 their centers are not collinear.
Output one line with the description of the required boundary: the coordinates of the center of the circle and its radius. Print as many digits after the decimal point as possible. The answer must be accurate to at least 10^{-5}.
The coordinates of the center and the radius of the circle must not exceed 10^7 in absolute value. It is guaranteed that a solution exists meeting these constraints.
Example 1