A16109 | 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.