A. Regular Bracket Sequencetime limit per test1 secondmemory limit per test512 megabytesinputstandard inputoutputstandard outputA 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 s of n 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.InputThe first line contains one integer t (1 \le t \le 1000) — the number of test cases.Each test case consists of one line containing s (2 \le |s| \le 100) — a sequence of characters (, ), and/or ?. There is exactly one character ( and exactly one character ) in this sequence.OutputFor 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).ExampleInput
5
()
(?)
(??)
??()
)?(?
Output
YES
NO
YES
YES
NO
NoteIn 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: ()().
5
()
(?)
(??)
??()
)?(?

YES NO YES YES NO 
['constructive algorithms', 'greedy', '*1000']