HZNUOJ

Three powers

Tags:   大数幂
Time Limit:  1 s      Memory Limit:   128 MB
Submission:5     AC:2     Score:99.85

Description

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

 

S = { 1, 3, 9, 27, 81, ... }

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.

 

Samples

input
1 7 14 783 1125900981634049 0
output
{ } { 3, 9 } { 1, 9, 27 } { 3, 9, 27, 6561, 19683 } { 59049, 3486784401, 205891132094649, 717897987691852588770249 }