CF1860A Not a Substring

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: - bracket sequences "()()" and "(())" are regular (they can be transformed into "(1)+(1)" and "((1+1)+1)", respectively); - bracket sequences ")(", "(" and ")" are not regular. 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 \le t \le 1000 $ ) — the number of test cases. The only line of each test case contains a string $ s $ ( $ 2 \le |s| \le 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.