Internet Problem Solving Contest

• This problem has no input files.

In the 24^th century, the humankind has conquered all the inner planets of the Solar System and it is slowly beginning to colonize the outer ones. Yet, they have not made any contact with extraterrestrial civilizations so far. This day, however, may give an answer to one of the oldest questions humans ever asked - "Are we alone in the universe?"

A group of four geo- and archeologists is exploring a very strange cave on Uranus. It is very deep and does not seem to be of natural origin. As soon as the first member of the team reaches the bottom, she shouts with an excitement - there is a door (clearly a sign of intelligent beings) with strange runes. Immediately they send a photo of the runes to the main lingo-analysis headquarters on the Earth. Surprisingly, the analysis is finished in a few minutes as the language is very similar to Latin. The runes (translated into English for your convenience) read:

Welcome, stranger! You have entered our major archive which is the most heavily guarded place on our planet. The single fact you are still alive means that we have already abandoned the land and went to the stars... or... our civilization might have been destroyed by a great cosmic catastrophe. In either case, be welcome. After you open this door, you will enter a big labyrinth consisting of five major parts, four of them made of seven smaller chambers. The last part is the most important - it hides a treasure of immense value - the highest wisdom of our civilization. First, however, you will need to prove you are worth it - you have to overcome a tiny (...ahem) obstacle. The chamber will open only if you correctly guess the time currently shown on the Big Clock. Its display consists of four digits (described below), the first two of them correspond to hours and the other two to minutes. Minutes increase by one until they reach 59 (the first digit corresponds to tens, the second to ones). The next minute increment increases hours and resets minutes back to zero. Hours go likewise, they increase by one (again, the first digit means tens, the second means ones), until the time reaches 11:59, when it wraps back to 00:00 on the next increment [translator's note: note that this is different from the two formats used on earth - the 24 hour format 0-23 and the 12 hour format 1-12]. If you think you know the time on the display, you can set it on the panel by the door leading to the main chamber and push the Big Red Button. If you set the right time, the chamber will reveal its secrets. However, if you set a wrong time... a little will remain of the whole planet... very little... Of course, this would be quite unfair (...heh), so we provide you with a few clues:

1. First, we have lied a little bit - you have ten guesses instead of just one, but should you guess wrong for the tenth time...
2. You might have wondered what the smaller chambers in the labyrinth are for. They are numbered 1 through 28 and look as follows:
   
   Each of them is connected to one segment of the Big Clock display. Whenever you set a time on the main panel and press the button, the chambers corresponding to active segments of the Big Clock flash with a bright light, whereas the other chambers remain dark. Active segments of the ten digits are shown in the following picture:

   0

   1

   2

   3

   4

   5

   6

   7

   8

   9

   [translator's note: strange, they use the same digits as we do]
3. Whenever the button gets pressed (and after the flash), the clock is advanced by a certain never-changing amount of time (expressed as an integer number of minutes) called Big Delta, which was calculated from several parameters of our planet. Apart from this advancement, the Big Clock's display does not change. However, we doubt you will be able to find the Big Delta yourself with your poor tools, so we give you a small hint - it is somewhere between 15 and 44 (inclusive).
4. If you are not confident enough to attempt this challenge, we have built a training facility on the next outer planet of this system [tn: probably Neptune], where you can test your skills in an easier environment. We were even generous enough to mount a device there which shows the Big Delta whenever you press the button (the Big Delta over there may be different from the Big Delta here). However, the reward is incomparable with the one you can find here.

Help the poor leader of scientists reveal the big secret of the ancient civilization by telling him what time he should try on the main panel and which chambers he should send his three colleagues to.

Formal specification

Neptune challenge corresponds to problem C1, Uranus is problem C2. Your submission should consist of two lines - the first line contains the time which is (in your opinion) currently shown on the Big Clock display (use hh:mm format). The second line containing at most three (remember, there are only four scientists in the cave and one has to remain at the main panel) numbers identifying the display segments.

The response will consist of:

• information on the guessed time (did the door open?)
• the state of the chambers (was there a light flash in the chamber?)
• the Big Delta (only on Neptune, C1)

Example

Example of a valid submission:

11:02
7 8

Example of the response:

7:flash 8:dark
The door remained closed, better luck next time!

Example of an invalid submission:

16:34
9 12

(the maximum possible time is 11:59).