House by the Road
The Ministry of Road Transport has decided to establish a new office. Since the minister frequently inspects the most crucial highways, it has been determined that the office should be situated not too far from these highways.
These key highways are represented as straight lines on a plane. The goal is to select a location for the office such that the maximum distance from the office to any of the highways is minimized.
Your task is to write a program that, given the layout of these important highways, identifies the optimal location for the Ministry of Road Transport's office.
Input
The first line of the input contains a single integer n — the number of the most important highways (1 ≤ n ≤ 10^4).
The following n lines describe the highways. Each highway is specified by four integers x_1, y_1, x_2, and y_2, representing a straight line passing through the points (x_1, y_1) and (x_2, y_2). The coordinates of these points do not exceed 10^4 in absolute value. The points (x_1, y_1) and (x_2, y_2) are distinct for each line.
Output
The output should consist of two real numbers separated by a space: the coordinates of the point where the Ministry of Road Transport's office should be located. The coordinates must not exceed 10^9 in absolute value, and it is guaranteed that at least one such solution exists. If there are multiple optimal solutions, any of them can be provided.
The answer must have an absolute or relative error of no more than 10^{-6}. This means that if the maximum distance from the output point to a highway is x, and in the correct answer it is y, the solution will be accepted if the expression |x - y| / max{1, |y|} does not exceed 10^{-6}.