Almost Regular Bracket Sequence

题意翻译

## Description 给定一个长度为 $n$ 的小括号序列，求有多少个位置满足将这个位置的括号方向反过来后使得新序列是一个合法的括号序列。即在任意一个位置前缀左括号的个数不少于前缀右括号的个数，同时整个序列左右括号个数相同 ## Input 第一行是一个整数 $n$ 代表序列长度 下面一行是括号序列 ## Output 输出一行一个数字代表的答案 ## Hint $1~\leq~n~\leq~10^6$

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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.

输入输出样例

输入样例 #1

6
(((())

输出样例 #1

3

输入样例 #2

6
()()()

输出样例 #2

0

输入样例 #3

1
)

输出样例 #3

0

输入样例 #4

8
)))(((((

输出样例 #4

0