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.

括号序列是由字符 '(' 和/或 ')' 组成的字符串。正则括号序列（regular bracket sequence）是指：通过在原序列的字符之间插入字符 '1' 和 '+'，可将其转化为一个合法的算术表达式的括号序列。例如：

• 括号序列 "()()" 和 "(())" 是正则的（它们可分别转化为 "(1)+(1)" 和 "((1+1)+1)"）；
• 括号序列 ")(", "(" 和 ")" 不是正则的。

给定一个括号序列 $s$；设其长度为 $n$。你的任务是：构造一个长度为 $2n$ 的正则括号序列 $t$，使得 $s$ 不作为连续子串出现在 $t$ 中；若不存在这样的序列，则报告无解。

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 ")".

第一行包含一个整数 $t$（$1 \le t \le 1000$）——测试用例的数量。

每个测试用例仅有一行，包含一个字符串 $s$（$2 \le |s| \le 50$），由字符 "(" 和/或 ")" 组成。

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.

对于每个测试用例，输出其答案。如果不存在所要求的合法括号序列，则在单独一行中输出 NO。否则，在第一行输出 YES，在第二行输出所要求的合法括号序列 $t$ 本身。如果存在多个满足条件的答案，你可以输出其中任意一个。