A. Not a Substringtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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.InputThe 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 ")".OutputFor 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.ExampleInput
4)((()()))()Output
YES
(())
YES
()()()
NO
YES
()(()())

4)((()()))()
YES (()) YES ()()() NO YES ()(()()) 
['constructive algorithms', 'strings', '*900']