According to Lewis Carroll, a clock that has stopped is more accurate than
one that is five minutes behind. He argues that the former is right twice
a day, whereas the latter never shows the correct time. Then again, a
clock that is always five minutes behind is in a sense perfectly accurate,
and therefore an extraordinary specimen. More usually, a clock is ahead or
behind because it runs at the wrong rate, so that its absolute discrepancy
from the true time is steadily changing. If left unregulated, such a
clock will show the true time at regular but perhaps lengthy intervals.
You are given two Strings of the form "hh:mm:ss".
The first represents exactly the true time, while the second is exactly
the time shown by an illtuned clock. This is an analog clock whose hour,
minute, and second hands sweep continuously around the dial at a speed
that is too fast or too slow by a constant factor. Both times are given
in the North American style, where the hour ranges between 1 and 12,
inclusive. Given an int specifying the nonzero number
of seconds that the clock gains every hour, calculate the number of
hours that elapse before it agrees with the true time. Your answer,
a double, must be correct with either absolute or relative precision of
1.0e9 (one billionth).
