E. Almost Regular Bracket Sequencetime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputPrint 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.ExamplesInput
6
(((())
Output
3
Input
6
()()()
Output
0
Input
1
)
Output
0
Input
8
)))(((((
Output
0

6
(((())

3 
['implementation', '*1900']