10118_TheClocks

Consider nine clocks arranged in a 3×3 array thusly:

 |-------|    |-------|    |-------|
 |       |    |       |    |   |   |
 |---O   |    |---O   |    |   O   |
 |       |    |       |    |       |
 |-------|    |-------|    |-------|
 A            B            C

 |-------|    |-------|    |-------|
 |       |    |       |    |       |
 |   O   |    |   O   |    |   O   |
 |   |   |    |   |   |    |   |   |
 |-------|    |-------|    |-------|
 D            E            F

 |-------|    |-------|    |-------|
 |       |    |       |    |       |
 |   O   |    |   O---|    |   O   |
 |   |   |    |       |    |   |   |
 |-------|    |-------|    |-------|
 G            H            I

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.

Each number represents a time accoring to following table:

9 9 12       9 12 12       9 12 12        12 12 12      12 12 12
6 6 6  5 ->  9  9  9  8->  9  9  9  4 ->  12  9  9  9-> 12 12 12
6 3 6        6  6  6       9  9  9        12  9  9      12 12 12

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

Multiple test cases, first line is an integer T, indecating the number of test cases. Each case has three lines:

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.

For each test case, 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).

2

9 9 12
6 6 6
6 3 6

12 9 12
9 9 9
12 9 12

4 5 8 9
5