Contest Pizza Cutting

In the fall of 2007 we ran a "Programming Contest Programming Contest", where the problems the contestants had to solve were about running a programming contest. The most important part of running a contest is the pizza.

The pizza is a circle of radius 1 with soy nuggets on top, and it is not cut yet. You have to cut it into slices under two conditions. Every slice has the same size, and every slice carries the same number of soy nuggets.

Cutting is restricted too. A cut runs along a straight line from the center of the circle to its circumference. A cut can never pass through a soy nugget, so every nugget always lies fully on one side of every cut.

Given the positions of the soy nuggets, write a program that finds the largest number of slices the pizza can be cut into under those rules. Leaving the pizza in one piece is always allowed, so a solution always exists.

The first line contains the number $K$ of data sets ($1 \le K \le 20$). $K$ data sets follow, each in this format.

The first line of a data set contains the number $N$ of soy nuggets on the pizza ($1 \le N \le 200$). Each of the next $N$ lines describes one nugget position in polar coordinates measured from the center of the pizza, given as two real numbers $\alpha$ and $r$ separated by a space. $\alpha$ is the counterclockwise angle between the positive $x$ axis and the segment from the center to the nugget, with $0 \le \alpha < 2\pi$. $r$ is the distance from the center to the nugget, with $0 < r \le 1$. The pizza has radius 1. Both numbers have at most 6 digits after the decimal point. Nuggets are points and no two nuggets lie on the same spot. Two nuggets can share an angle when their distances from the center differ.

For each data set, print Data Set x: on a line of its own, where $x$ is the number of the data set counting from 1. On the next line print y slices, where $y$ is the largest number of slices. Print 1 slices when the largest number is 1. Print one blank line after each data set.