Problem Statement

There are $N$ line segments in a coordinate plane, and the $i$-th line segment $(1\leq i\leq N)$ has two points $(a _ i,b _ i)$ and $(c _ i,d _ i)$ as its endpoints. Here, each line segment includes its endpoints. Additionally, no two line segments share a point.

We want to place a single closed disk in this plane so that it shares a point with each line segment. In other words, we want to draw a single circle so that each line segment shares a point with either the circumference of the circle or its interior (or both). Find the smallest possible radius of such a disk.

Constraints

• $2\leq N\leq 100$
• $0\leq a _ i,b _ i,c _ i,d _ i\leq1000\ (1\leq i\leq N)$
• $(a _ i,b _ i)\neq(c _ i,d _ i)\ (1\leq i\leq N)$
• The $i$-th and $j$-th line segments do not share a point $(1\leq i\lt j\leq N)$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
a _ 1 b _ 1 c _ 1 d _ 1
a _ 2 b _ 2 c _ 2 d _ 2
\vdots
a _ N b _ N c _ N d _ N

Output

Print the answer in a single line. Your output will be considered correct when the absolute or relative error from the true value is at most $10 ^ {−5}$.