A12343 | Almost Regular Bracket Sequence

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.

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.

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.