House by the Road#2187
The Department of Transport has decided to build a new office. Since the minister regularly inspects the most important highways, it has been decided that the office should not be located too far from them.
The most important highways are represented as straight lines on a plane. The Department wants to choose a location for its office such that the maximum distance from the office to any highway is minimized.
You are required to write a program that, given the locations of the most important highways, determines the optimal location for the Department of Transport's office.
The first line contains an integer (1 \leq n \leq 10^4) — the number of most important highways.
The following lines describe the highways. Each highway is given by four integers x_1, y_1, x_2, and y_2, representing a straight line passing through points (x_1, y_1) and (x_2, y_2). The absolute values of the coordinates do not exceed 10^4. For no line do the points (x_1, y_1) and (x_2, y_2) coincide.
Output two real numbers separated by a space — the coordinates of the point where the Department of Transport's office should be located. The absolute values of the coordinates must not exceed 10^9, and it is guaranteed that at least one such solution exists. If there are several optimal answers, print any of them.
The answer must have an absolute or relative error of no more than 10^{-6}. This means the following: let be the maximum distance from the printed point to a highway, and this value in the correct answer. The answer will be accepted if \frac{|x-y|}{\max\{1, |y|\}} \leq 10^{-6}.
Example 1