Online JudgeProblem SetAuthorsOnline ContestsUser
Web Board
Home Page
Statistical Charts
Submit Problem
Online Status
Update your info
Authors ranklist
Current Contest
Past Contests
Scheduled Contests
Award Contest
User ID:
Necklace Decomposition
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 1003Accepted: 366


The set of cyclic rotations of a string are the strings obtained by embedding the string clockwise on a ring, with the first character following on the last, starting at any character position and moving clockwise on the ring until the character preceeding the starting character is reached. A string is a necklace if it is the lexicographically smallest among all its cyclic rotations. For instance, for the string 01011 the cyclic rotations are (10110,01101,11010,10101,01011), and furthermore 01011 is the smallest string and hence, a necklace.
Any string S can be written in a unique way as a concatenation S = T1T2 . . . Tk of necklaces Ti such that Ti+1 < Ti for all i = 1, . . . , k - 1, and TiTi+1 is not a necklace for any i = 1, . . . , k - 1. This representation is called the necklace decomposition of the string S, and your task is to find it.
The relation < on two strings is the lexicographical order and has the usual interpretation: A < B if A is a proper prefix of B or if A is equal to B in the first j - 1 positions but smaller in the jth position for some j. For instance, 001 < 0010 and 1101011 < 1101100.


On the first line of the input is a single positive integer n, telling the number of test scenarios to follow. Each scenario consists of one line containing a non-empty string of zeros and ones of length at most 100.


For each scenario, output one line containing the necklace decomposition of the string. The necklaces should be written as '(' necklace ')'.

Sample Input


Sample Output



[Submit]   [Go Back]   [Status]   [Discuss]

Home Page   Go Back  To top

All Rights Reserved 2003-2013 Ying Fuchen,Xu Pengcheng,Xie Di
Any problem, Please Contact Administrator