Sun Bathing

Lying in the sand is the favorite beach activity for many people. Because prolonged sun exposure causes painful sunburns, many sunbathers lie under a parasol to shield themselves from the sun's rays. If you know the time window during which you will lie on the beach, where should you place the parasol to protect as much of your body as possible?

Here we answer a slightly easier question. Given the positions of your body and the parasol, compute what percentage of your body is exposed to the sun for at least part of the time.

For simplicity, model your body as a rectangle of size $w \times h$ centimeters. Treat the beach as a two-dimensional plane with the origin at the center of your body. The side of length $h$ runs along the feet-to-head direction, and the side of length $w$ runs across your body. The parasol is a circle of radius $r$, mounted horizontally at height $d$ above your body, with its center also above the origin.

You sunbathe from the moment the sun makes an angle $\alpha_1$ with the beach to the moment it makes an angle $\alpha_2$, where $1^\circ \le \alpha_1 < \alpha_2 \le 179^\circ$. Assume the sun is a single point infinitely far away and travels in a straight line from your feet to your head (not from one arm to the other).

The first line contains an integer $K \ge 1$, the number of data sets. Each of the following $K$ lines describes one data set and contains, in this order, the real numbers $w$, $h$, $r$, $d$, $\alpha_1$, $\alpha_2$ (the two angles are given in degrees). The sun moves from your feet to your head, i.e. parallel to the side of length $h$, and never parallel to the side of length $w$.

For each data set, first print a line Data Set x:, where $x$ is the data set number starting from $1$. On the next line, print the percentage of your body that is exposed to the sun at some moment during the interval, rounded to exactly two decimal places and followed by a percent sign (for example, 0.00%).