Rails#2499
An important parameter of a railway is the track gauge — the distance between the two rails on which a train travels. This parameter determines the types of trains and machines that can operate on the railway.
Recently, a space expedition to planet RCC-0805 discovered railways on this planet. A railway depot was even found, but the track gauge has not yet been determined. The problem is that the railways on this planet were laid without sleepers, so it is not always easy to determine which rails correspond to each other.
You are given a plan of the rail layout at the railway depot. For simplicity, assume the area is an infinite plane, and each rail is represented as a straight line. You need to find the minimum possible track gauge such that the rails can be divided into pairs so that each pair consists of parallel rails at distance from each other.
The first line contains an integer (1 \leq n \leq 2000). Each of the following lines contains four integers x_{i, 1}, y_{i, 1}, x_{i, 2}, y_{i, 2} — the coordinates of two distinct points through which the rail passes. All coordinates do not exceed in absolute value. The lines corresponding to different rails are not coincident.
Output a real number — the minimum possible track gauge. It must be found with accuracy at least 10^{-6}.
If it is impossible to pair the rails at any track gauge while meeting the requirements, output the number .
Example 1