题目描述

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.

 

样例 1

输入

1
7
14
783
1125900981634049
0

输出

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

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题目来源：fps-zhblue-waterloo-040612.xml；FPS 共享题包，题包内第 2 题。保留原作者与原赛事署名。