Clock Puzzle

Problem Background

Special for beginners, ^_^

Problem Description

There are $9$ clocks arranged in a $3 \times 3$ matrix:

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

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

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

Now we want to use the minimum number of moves to set all $9$ clock hands to the $12$ o'clock position. There are $9$ different kinds of moves allowed. As shown in the table below, each move rotates the hands of several clocks $90^\circ$ clockwise.

move    clocks affected
 1         ABDE
 2         ABC
 3         BCEF
 4         ADG
 5         BDEFH
 6         CFI
 7         DEGH
 8         GHI
 9         EFHI

Input Format

$9$ integers, the starting positions of each clock's hand, separated by single spaces.

Here $0 = 12$ o'clock, $1 = 3$ o'clock, $2 = 6$ o'clock, $3 = 9$ o'clock.

Output Format

Output a shortest sequence of moves that makes all $9$ clock hands point to $12$ o'clock. Output the move numbers in increasing order, separated by single spaces.

Sample Input

3 3 0
2 2 2
2 1 2

Sample Output

4 5 8 9

Constraints

Time limit: 1s, memory limit: 1024KiB for each test case.