1394 -- Perfect Time
Time Limit :1000 MS Memory Limit :65536 KB
Accepts : 63 Submits : 145
User Accepts : 53 User Submits : 57
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Description

Alpc62 has a hobby — focusing on one thing for a long time. This habit makes Alpc62 find many interesting things, such as three hands of Windows XP Clock are superpositions sometimes.
To record his “great” discover, one day from 00:00:00 to 11:59:59, Alpc62 focused on the clock for the full twelve hours and at last he got all time of the superposition:
00:00:00 01:05:05 02:10:10 03:16:16 04:21:21 05:27:27
06:32:32 07:38:38 08:43:43 09:49:49 10:54:54 11:59:59
Twelve such time point in all.
Furthermore Alpc62 discovers the turning rule of the Windows XP Clock:
  1. Each hand of Windows XP Clock must obey the turn rate principle of 6 degree per move.
  2. Second hand makes one move per second.
  3. Minute hand makes one move per minute.
  4. Hour hand makes one move twelve minutes.
 
Suddenly, Alpc62 gets a discovery of making a definition of “Perfect Time”:
Three hands regarded as three straight lines, if one line is the bisector of the other two lines, this time is a “Perfect Time”, such as 00:00:00, 11:48:10, 11:53:26, and etc.
ALPC62 is so exhausted that he cannot focus on the clock any longer. He has to have a rest.
If you can find and record all “Perfect Time” from 00:00:00 to 11:59:59, the great discovery will belong to you but not Alpc62. Take a chance!
Note: you must treat the hand lines as ray lines.

Input

This Problem has No input.
 

Output

Output all “Perfect Time” from 00:00:00 to 11:59:59 according to the time order. One time for each line, the format is as follow:
xx:xx:xx

Sample Input

 

Sample Output

00:00:00
00:00:30
00:01:02
00:01:59
00:02:01
......

Hint

Sample Output just shows the example format for you, your output cannot contain suspension point (......).

Source

Alpc NUDT campus contest 2009
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