Consider a classical 2-arm 12-hour clock. Now imagine a really precise one. One that
can indicate the time in hours, minutes, seconds, and hundredths of a second. Such
clock can specify the time
between 0:0:0.00 and 11:59:59.99 inclusive. (We’ll use the format
hour:minute:second.hundredths) to write the time displayed on such clock. Now, you
are given two identical clocks of this type, each of them showing some time where the
first is strictly before the second. You also know the radius of the clock face. We’re
interested in computing the area of the clock face determined by the two small (hour)
clock-arms on the two clocks. The area starts from the position of the first hour clockarm
and continues in the clockwise way till the position of the second hour clock-arm.
Input Format
Your program will be tested on one or more test cases. The first line in the input
specifies a single integer D representing the number of test cases.
The first line will be followed by D test cases, where each case is specified on three
lines. The first line in a test case specifies four integers denoting the time on the first
clock using the following format:
H M S U with H for hours, M for minutes, S for seconds, and U for hundredth of a
second. Note that 0 ≤H <12, 0 ≤M <60, 0 ≤ S < 60, and 0 ≤U <100.
The second line of a test case specifies the time on the second clock, using the same
format as the first.
The third line specifies a real number denoting the radius of the clock. The maximum
for the radius is 10,000.