Consider nine magical clocks of CodeVillage arranged in a 3x3 array like:
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.
Move Affected clocks
Each number represents a time accoring to following table:
[But this might or might not be the `correct' answer; see below.] INPUT
Line 0 contains t.
Then t testcases with 3 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. SAMPLE INPUT
9 9 12
6 6 6
6 3 6 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 OUTPUT
4 5 8 9