SP666 VOCV - Con-Junctions

The city of **Y-O** is a network of two-way streets and junctions with the following properties: 1. There is no more than one street between each pair of junctions. 2. Every junction is connected to every other junction either directly via a street or through other junctions by a unique path. 3. When a light is placed at a junction, all the streets meeting at this junction are also lit. A valid lighting is a set of junctions such that if lights were placed at these, all the streets would be lit. An optimal lighting is a valid lighting such that it contains the least number of junctions. The task is divided into two subtasks: 1. Find the number of lights in an optimal lighting. 2. Find the total number of such optimal lightings in the city.

- The first line of the input contains a positive integer **t

The output must consist of **t** lines, the **k $ ^{th} $** line corresponding to the **k $ ^{th} $** network; **(1