Almost Regular Bracket Sequence

3000ms

262144K

Description:

You are given a bracket sequence $$$s$$$ consisting of $$$n$$$ opening '(' and closing ')' brackets.

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 "()()", "(())" are regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.

You can change the type of some bracket $$$s_i$$$. It means that if $$$s_i = $$$ ')' then you can change it to '(' and vice versa.

Your task is to calculate the number of positions $$$i$$$ such that if you change the type of the $$$i$$$-th bracket, then the resulting bracket sequence becomes regular.

Input:

The first line of the input contains one integer $$$n$$$ ($$$1 \le n \le 10^6$$$) — the length of the bracket sequence.

The second line of the input contains the string $$$s$$$ consisting of $$$n$$$ opening '(' and closing ')' brackets.

Output:

Print one integer — the number of positions $$$i$$$ such that if you change the type of the $$$i$$$-th bracket, then the resulting bracket sequence becomes regular.

Sample Input:

6
(((())

Sample Output:

Sample Input:

6
()()()

Sample Output:

Sample Input:

1
)

Sample Output:

Sample Input:

8
)))(((((

Sample Output:

Informação

Provedor Codeforces

Código CF1095E