B'A bracket sequence is a string consisting of characters '( ' and/or ') '. A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1 ' and '+ ' between the original characters of the sequence. For example: You are given a bracket sequence s ; let 's define its length as n . Your task is to find a regular bracket sequence t of length 2n such that s does not occur in t as a contiguous substring, or report that there is no such sequence. The first line contains a single integer t ( 1 <= t <= 1000 ) -- the number of test cases. The only line of each test case contains a string s ( 2 <= |s| <= 50 ), consisting of characters "(" and/or ")". For each test case, print the answer to it. If there is no required regular bracket sequence, print NO in a separate line. Otherwise, print YES in the first line, and the required regular bracket sequence t itself in the second line. If there are multiple answers -- you may print any of them. '...