This is yet another problem dealing with regular bracket sequences.

We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not. 

You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 10<sup class="upper-index">6</sup>.
s = input()
stack = [-1]  # initialize stack with -1
ans = 0

for i in range(len(s)):
    if s[i] == "(":
        stack.append(i)  # push index of opening bracket
    elif len(stack) > 1:
        stack.pop()  # pop index of matching opening bracket
        ans = max(ans, i - stack[-1])  # update length of longest sequence

print(ans)
