write a go solution for Description:
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.

Input Format:
The first line of input contains a string s (1<=|s|<=5*10^5) — the bracket sequence.

It is guaranteed that s only contains the characters "(" and ")".

Output Format:
Output a single integer — the number of ways to remove k characters from s so that s becomes balanced, modulo 998,244,353.

Note:
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.

- texttt(colorRedtexttt)texttt)colorRedtexttt(texttt(texttt),
- texttt(texttt)colorRedtexttt)colorRedtexttt(texttt(texttt),
- texttt(colorRedtexttt)texttt)texttt(colorRedtexttt(texttt),
- texttt(texttt)colorRedtexttt)texttt(colorRedtexttt(texttt).

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.. Output only the code with no comments, explanation, or additional text.