CF1095E.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.

给你一个由 $n$ 个左括号 '(' 和右括号 ')' 组成的括号序列 $s$。

合法括号序列（regular bracket sequence）是指：通过在原序列的字符之间插入字符 '1' 和 '+'，可将其转化为一个正确的算术表达式。例如，括号序列 "()()" 和 "(())" 是合法的（对应表达式分别为 "(1)+(1)" 和 "((1+1)+1)"），而 ")(" 和 "(" 则不是。

你可以将某个位置 $s_i$ 上的括号类型进行翻转：即若 $s_i = $ ')'，则可将其改为 '('；反之亦然。

你的任务是：计算满足如下条件的位置 $i$ 的个数——即若将第 $i$ 个括号的类型翻转，则所得括号序列成为合法括号序列。

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.

输入的第一行包含一个整数 $n$（$1 \le n \le 10^6$）——括号序列的长度。

输入的第二行包含一个由 $n$ 个左括号 '(' 和右括号 ')' 组成的字符串 $s$。

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.

输出一个整数——即满足如下条件的位置 $i$ 的个数：若将第 $i$ 个括号的类型进行翻转，则所得括号序列变为合法序列。