Time Limit: 1 s
Memory Limit: 128 MB

Submission：5
AC：2
Score：99.85

Consider the set of all non-negative integer powers of 3.

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.

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.

input

1
7
14
783
1125900981634049
0

output

{ }
{ 3, 9 }
{ 1, 9, 27 }
{ 3, 9, 27, 6561, 19683 }
{ 59049, 3486784401, 205891132094649, 717897987691852588770249 }