A. Not a Substring
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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 ")".

Output

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.

Example
Input
4
)(
(()
()
))()
Output
YES
(())
YES
()()()
NO
YES
()(()())