Problem: A bracket sequence is called regular if it is possible to obtain correct arithmetic expression by inserting characters + and 1 into this sequence. For example, sequences (())(), () and (()(())) are regular, while )(, (() and (()))( are not. Let's call a regular bracket sequence "RBS".
You are given a sequence of characters (, ), and/or ?. There is exactly one character ( and exactly one character ) in this sequence.
You have to replace every character ? with either ) or ( (different characters ? can be replaced with different brackets). You cannot reorder the characters, remove them, insert other characters, and each ? must be replaced.
Determine if it is possible to obtain an RBS after these replacements.
Input Format: The first line contains one integer () — the number of test cases.
Each test case consists of one line containing () — a sequence of characters (, ), and/or ?. There is exactly one character ( and exactly one character ) in this sequence.
Output Format: For each test case, print YES if it is possible to obtain a regular bracket sequence, or NO otherwise}.
You may print each letter in any case (for example, YES, Yes, yes, yEs will all be recognized as positive answer).
Note: In the first test case, the sequence is already an RBS.
In the third test case, you can obtain an RBS as follows: ()() or (()).
In the fourth test case, you can obtain an RBS as follows: ()().