The Clocks

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

    Consider nine clocks arranged in a 3x3 array thusly:
 
    The goal is to find a minimal sequence of moves to return all the dials to 12 o\'clock. Nine different ways to turn the dials on the clocks are supplied via a table below; each way is called a move. Select for each move a number 1 through 9 which will cause the dials of the affected clocks (see next table) to be turned 90 degrees clockwise.  

Example
 

[But this might or might not be the `correct\' answer; see below.]

 

Input

    There are multiple test cases. 
    For each test case:

 

Lines 1-3:

Three lines of three space-separated numbers; each number represents the start time of one clock, 3, 6, 9, or 12. The ordering of the numbers corresponds to the first example above.

Output

     A single line that contains a space separated list of the shortest sequence of moves (designated by numbers) which returns all the clocks to 12:00. If there is more than one solution, print the one which gives the lowest number when the moves are concatenated (e.g., 5 2 4 6 < 9 3 1 1).

Sample Input

9 9 12
6 6 6
6 3 6

Sample Output

4 5 8 9

Hint

 

Source