## IPSC 2006

## Problem Q – Labyrinth

Fred is a robotic mouse built by a group of students of
artificial intelligence. Fred can move around in the labyrinth shown
in the picture below. Whenever Fred comes to a place marked by a
number, he has to choose one of the possible directions. Behavior of the
mouse should look chaotic and complex enough so that it will impress
students' supervisor.

+--------4
| |
| 8--9 |
| | | |
2--7--0 |
| | |
1 6-----+

Numbered places in the labyrinth are called nodes. Fred has
one integer *X* stored in its memory and can perform some
calculations. In each node (except node 1) he chooses
a direction according to *X*, decreases *X* by 1
and goes to the chosen node. The direction is chosen according to
this rules:

**Node 2:** Compute X mod 3.
If the result is 0, go to 7
1, go to 1
2, go to 4.
**Node 4:** Let Y be X written backwards (in decimal system).
If Y>X then go to 6 otherwise go to 2.
**Node 6:** Compute the number of digits of X (in decimal system).
If the result is even then go to 4 otherwise go to 7.
**Node 7:** Compute (X*X) mod 7.
If the result is 0 go to 2
1 go to 6
2 go to 8
4 go to 0.
**Node 8:** Compute X mod 5.
If the result is 2 or 3 then go to 7 otherwise go to 9.
**Node 9:** If you have come from 8 then go to 0.
If you have come from 0 then go to 8.
**Node 0:** Let Y be the third least significant digit of X in decimal system
(if X<100 then Y=0). If Y<=7 then go to 7 otherwise go to 9.

At the beginning of each experiment, the experimenter puts the
mouse in the node 0 and initializes value *X* by voice.
After that, the mouse starts to move. The mouse displays current value of
*X* on its digital display. The experiment finishes when the mouse
enters the node 1, the result of the experiment is the number displayed. If
the value of *X* decreases to zero, the experiment fails and its
result is -1.

### Input specification

The input file contains
several initial values of *X* as they were told by
the experimenter.

### Output specification

For each value of *X*
in the input file write to a separate line of the output file the
result of the corresponding experiment (see example output).

### Example

**Input:**
thirteen
fourteen
one-thousand

**Output:**
-1
9
789