#描述#
We can number binary trees using the following scheme:
The empty tree is numbered 0.
The single-node tree is numbered 1.
All binary trees having m nodes have numbers less than all those having m+1 nodes.
Any binary tree having m nodes with left and right subtrees L and R is numbered n such that all trees having m nodes numbered > n have either
Left subtrees numbered higher than L, or
A left subtree = L and a right subtree numbered higher than R.
The first 10 binary trees and tree number 20 in this sequence are shown below:

Your job for this problem is to output a binary tree when given its order number.

#格式#
##输入格式##
Input consists of multiple problem instances. Each instance consists of a single integer n, where 1 &lt= n &lt= 500,000,000. A value of n = 0 terminates input. (Note that this means you will never have to output the empty tree.)

##输出格式##
For each problem instance, you should output one line containing the tree corresponding to the order number for that instance. To print out the tree, use the following scheme:
A tree with no children should be output as X.
A tree with left and right subtrees L and R should be output as (L')X(R'), where L' and R' are the representations of L and R.
If L is empty, just output X(R').
If R is empty, just output (L')X.

#样例1#
##样例输入1##

1
20
31117532
0

##样例输出1##

X
((X)X(X))X
(X(X(((X(X))X(X))X(X))))X(((X((X)X((X)X)))X)X)

#限制#
1000ms
32768KB

#提示#

#来源#
WY