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.
The input file contains several initial values of X as they were told by the experimenter.
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).
thirteen fourteen one-thousandOutput:
-1 9 789