In the event of technical difficulties with Szkopuł, please contact us via email at [email protected].

If you would like to talk about tasks, solutions or technical problems, please visit our Discord servers. They are moderated by the community, but members of the support team are also active there.

Little Johnny - a well-respected young mathematician - has a younger sister, Justina. Johnny likes his
sister very much and he gladly helps her with her homework, but, like most scientific minds, he does mind
solving the same problems again. Unfortunately, Justina is a very diligent pupil, and so she asks Johnny to
review her assignments many times, for sake of certainty. One sunny Friday, just before the famous Long
May Weekend^{1} the math teacher gave many exercises consisting in finding the axes of symmetry of various
geometric figures. Justina is most likely to spend considerable amount of time solving these tasks. Little
Johnny had arranged himself a trip to the seaside long time before, nevertheless he feels obliged to help his
little sister. Soon, he has found a solution - it would be best to write a programme that would
ease checking Justina's solutions. Since Johnny is a mathematician, not a computer scientist, and you are his
best friend, it falls to you to write it.

Write a programme that:

- reads the descriptions of the polygons from the standard input,
- determines the number of axes of symmetry for each one of them,
- writes the result to the standard output.

In the first line of the input there is one integer () - it is the number of polygons, for which the number of axes of symmetry is to be determined. Next, descriptions of the polygons follow. The first line of each description contains one integer () denoting the number of vertices of the polygon. In each of the following lines there are two integers and () representing the coordinates of subsequent vertices of the polygon. The polygons need not be convex, but they have no self-intersections - any two sides have at most one common point - their common endpoint, if they actually share it. Furthermore, no pair of consecutive sides is parallel.

Your programme should output exactly lines, with the 'th line containing a sole integer - the number of axes of symmetry of the 'th polygon.

For the input data:

2 12 1 -1 2 -1 2 1 1 1 1 2 -1 2 -1 1 -2 1 -2 -1 -1 -1 -1 -2 1 -2 6 -1 1 -2 0 -1 -1 1 -1 2 0 1 1

the correct result is:

4 2

1. In Poland, there is an accumulation of public and national holidays in the beginning of May. Those are: 1

*Task author: Piotr Stanczyk.*