The Euclidean Clock

Consider a classic two-handed 12-hour clock, but a very precise one that can show the time in hours, minutes, seconds, and hundredths of a second. Such a clock can display any time from 0:0:0.00 up to 11:59:59.99 inclusive (we write times in the format hour:minute:second.hundredths).

You are given two identical clocks of this kind. The time shown on the first clock is strictly earlier than the time shown on the second. You are also given the radius of the clock face. Consider only the small (hour) hands of the two clocks. Starting from the position of the first clock's hour hand and sweeping clockwise until the position of the second clock's hour hand, these two hour-hand positions cut out a sector of the clock face. Compute the area of that sector.

Because both times lie within a single 12-hour period and the first time is strictly earlier, the second clock's hour hand is always further along in the clockwise direction than the first, so the swept sector never wraps past a full revolution and is always well defined.

The first line contains a single integer $D$, the number of test cases. Each test case is then given on three lines.

The first line of a test case contains four integers describing the time on the first clock:

H M S U

where $H$ is hours, $M$ is minutes, $S$ is seconds, and $U$ is hundredths of a second, with $0 \le H < 12$, $0 \le M < 60$, $0 \le S < 60$, and $0 \le U < 100$.

The second line gives the time on the second clock in the same format.

The third line contains a real number: the radius of the clock. The radius is at most 10,000.

For each test case, print one line in the format

k. f

where $k$ is the test case number (starting from $1$) and $f$ is the answer rounded to three decimal places.