Hadron Colliders
Two countries, Bytelandia and Flatlandia, have teamed up for high-energy physics research and have constructed n hadron colliders. Each collider is circular and located underground, with an extremely small thickness, allowing them to be treated as circles.
Given the complexity of maintaining these hadron colliders, neither country wants to handle all the maintenance alone. Therefore, they agreed to split the maintenance of each collider equally. To achieve this, they decided that each country would be responsible for exactly half of each collider. The boundary dividing the zones of responsibility should be a circle that intersects each collider at two diametrically opposite points, effectively splitting each collider into two equal halves.
Your task is to write a program that, given the descriptions of the colliders, finds a circle that fulfills these requirements.
Input
The first line of the input contains an integer n (1 ≤ n ≤ 3). Each of the following n lines provides the description of one collider. Each description includes three integers: x, y, r, representing the coordinates of the center of the collider and its radius (|x|, |y| ≤ 1000, 1 ≤ r ≤ 1000). The colliders do not overlap, do not lie inside one another, and if n=3, their centers are not collinear.
Output
The output should be a single line describing the required boundary: the coordinates of the center of the circle and its radius. Provide as many decimal places as possible, ensuring the answer is accurate to at least 10^{-5}.
The coordinates of the center and the radius of the circle should not exceed 10^7 in absolute value. It is guaranteed that a solution exists that meets these constraints.