## CLOCKS - The Clocks

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`|-------|    |-------|    |-------|    |       |    |       |    |   |   |    |---O   |    |---O   |    |   O   |          |       |    |       |    |       |           |-------|    |-------|    |-------|        A            B            C|-------|    |-------|    |-------||       |    |       |    |       ||   O   |    |   O   |    |   O   ||   |   |    |   |   |    |   |   ||-------|    |-------|    |-------|    D            E            F|-------|    |-------|    |-------||       |    |       |    |       ||   O   |    |   O---|    |   O   ||   |   |    |       |    |   |   ||-------|    |-------|    |-------|  (Figure 1)    G            H            I`

There are nine clocks in a 3*3 array (figure 1). The goal is to return all the dials to 12 o'clock with as few moves as possible. There are nine different allowed ways to turn the dials on the clocks. Each such way is called a move. Select for each move a number 1 to 9. That number will turn the dials 90' (degrees) clockwise on those clocks which are affected according to figure 2 below.

`Move   Affected clocks  1         ABDE 2         ABC 3         BCEF 4         ADG 5         BDEFH 6         CFI 7         DEGH 8         GHI 9         EFHI    (Figure 2)`

### Input

Read nine numbers from standard input. These numbers give the start positions of the dials. 0=12 o'clock, 1=3 o'clock, 2=6 o'clock, 3=9 o'clock. The example in figure 1 gives the following input data file:

`3 3 02 2 2 2 1 2`

### Output

Write to the standard output the shortest sequence of moves (numbers), which returns all the dials to 12 o'clock. In case there are many solutions, write the solution which is the least in lexicographic order. In our example the output is as follows:

`4 5 8 9`

### Example

```Each number represents a time accoring to following table:0 = 12 o'clock1 = 3 o'clock2 = 6 o'clock 3 = 9 o'clock

3 3 0         3 0 0         3 0 0          0 0 0         0 0 0 2 2 2   5->   3 3 3   8->   3 3 3   4 ->   0 3 3   9->   0 0 0 2 1 2         2 2 2         3 3 3          0 3 3         0 0 0 Note: This just represents a valid sequence of moves, and not the solution
```

hide comments ALi Ibrahim: 2015-08-08 10:55:52 First Accepted :) mehmetin: 2014-02-16 14:16:42 --- Last edit: 2014-02-16 14:37:05 shiva_hellgeek: 2013-05-30 13:51:46 I used the worst possible method to solve this problem. Solved the entire problem on paper. :p

 Added by: bsrk Date: 2010-08-22 Time limit: 0.25s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: NODEJS OBJC PERL6 VB.NET Resource: IOI 94 - Day 2