B'Chiyuu has a bracket sequence ^ dagger s of length n . Let k be the minimum number of characters that Chiyuu has to remove from s to make s balanced ^ ddagger . Now, Koxia wants you to count the number of ways to remove k characters from s so that s becomes balanced, modulo 998 ,244 ,353 . Note that two ways of removing characters are considered distinct if and only if the set of indices removed is different. ^ dagger A bracket sequence is a string containing only the characters "(" and ")". ^ ddagger A bracket sequence is called balanced if one can turn it into a valid math expression by adding characters + and 1. For example, sequences (())(), (), (()(())) and the empty string are balanced, while )(, ((), and (()))( are not. The first line of input contains a string s ( 1 <= q |s| <= q 5 cdot {10}^5 ) -- the bracket sequence. It is guaranteed that s only contains the characters "(" and ")". Output a single integer -- the number of ways to remove k characters from s so that s becomes balanced, modulo 998 ,244 ,353 . In the first test case, it can be proved that the minimum number of characters that Chiyuu has to remove is 2 . There are 4 ways to remove 2 characters to make s balanced as follows. Deleted characters are noted as red. In the second test case, the only way to make s balanced is by deleting the only character to get an empty bracket sequence, which is considered balanced. '...