Consider the set of all non-negative integer powers of 3.
$S = \{ 1, 3, 9, 27, 81, \ldots \} $
Consider the sequence of all subsets of $S$ ordered by the value of the sum of their elements. The question is simple: find the set at the $n$-th position in the sequence and print it in increasing order of its elements.
Each line of input contains a number $n$, which is a positive integer with no more than $19$ digits. The last line of input contains $0$ and it should not be processed. There are at most $100$ test cases.
For each line of input, output a single line displaying the $n$-th set as described above, in the format used in the sample output.
Sample Input 1 | Sample Output 1 |
---|---|
1 7 14 783 1125900981634049 0 |
{ } { 3, 9 } { 1, 9, 27 } { 3, 9, 27, 6561, 19683 } { 59049, 3486784401, 205891132094649, 717897987691852588770249 } |