Secret Island Base

A group of ninjas wants to establish a new secret base for training. For its location they have picked a remote cluster of islands. To keep the base as hidden as possible, they want to build it as far from the coast as they can.

They have asked you to help them evaluate each island. Every island is modeled as a polygon in the plane, and its boundary is the coastline. For each island, determine the greatest possible distance from the coastline at which one can stand while remaining on the island. The distance from a point to the coastline is the shortest straight-line (Euclidean) distance from that point to any point on the coastline.

Equivalently, for each island you must find the radius of the largest circle that fits entirely inside the polygon.

Naturally, this has to stay a secret, so do not discuss it with anyone.

The first line contains a single integer: the number of islands that follow. Each island is described as follows:

• One line with an integer $N$ where $3 \le N \le 20$: the number of vertices of the polygon that describes the island's coastline.
• $N$ lines, each with two integers $x$ and $y$ where $-100 \le x, y \le 100$: the coordinates of a vertex.

The vertices of each polygon are listed in counterclockwise order.

For each island, output a single line with the largest distance from the coastline that a point on the island can achieve, rounded to exactly $3$ decimal places.