Scales

Give you a scale, a goods weigts m kilograms. And then give you some stones weighting 1, 3, 9, 27, ..., 3^k. Of course, the number of different weights' is only ONE.

Now put the goods on the left of scale. And then you should put some stones on two sides of scale to make the scale balanced.

An integer m, stands for the weights of the goods (0 ≤ m ≤ 100 000 000)

You should output two lines.

In the first line, the first integer N1 is the number of stones putting on the left of scale, and then N1 integers follow(in the ascend order), indicating the weight of stones putting on the left, seperated by one space. In the second line, please use the same way as the first line's to output the N2, which is the number of stones putting on the right side. Then following N2 integers, which are in ascending order, indicate the stones' weight putting on the right side.

42
30

3 3 9 27
1 81
0
2 3 27

2009 Multi-University Training Contest 6 - Host by WHU