One of the first atomic clocks was an ammonia-controlled clock. It was built in 1949 at the National Bureau of Standards, Washington, D.C.; in this clock the frequency did not vary by more than one part in 108.
Nuclear clocks are built using two clocks. The aggregate of atoms that emit the gamma radiation of precise frequency may be called the emitter clock; the group of atoms that absorb this radiation is the absorber clock. One pair of these nuclear clocks can detect energy changes of one part in 1014, being about 1,000 times more sensitive than the best atomic clock.
The cesium clock is the most accurate type of clock yet developed. This device makes use of transitions between the spin states of the cesium nucleus and produces a frequency which is so regular that it has been adopted for establishing the time standard.
The history of clocks is fascinating, but unrelated to this problem. In this problem, you are asked to find the angle between the minute hand and the hour hand on a regular analog clock. Assume that the second hand, if there were one, would be pointing straight up at the 12. Give all angles as the smallest positive angles. For example 9:00 is 90 degrees; not -90 or 270 degrees.
The input is a list of times in the form ‘H:M ’, each on their own line, with 1 ≤ H ≤ 12 and 00 ≤ M ≤ 59. The input is terminated with the time ‘0:00’. Note that H may be represented with 1 or 2 digits (for 1–9 or 10–12, respectively); M is always represented with 2 digits (the input times are what you typically see on a digital clock).
The output displays the smallest positive angle in degrees between the hands for each time. The answer should between 0 degrees and 180 degrees for all input times. Display each angle on a line by itself in the same order as the input. The output should be rounded to the nearest 1/1000, i.e., three places after the decimal point should be printed.