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>.
#!/usr/bin/env python


def main():
    balance = longest = current = 0
    count = 1
    for p in input():
        current += 1
        if p == "(":
            balance += 1
        else:
            balance -= 1
            if balance > 0:
                continue
            if balance == 0:
                if current > longest:
                    longest = current
                    count = 1
                elif current == longest:
                    count += 1
            current = balance = 0
    print(longest, count)


if __name__ == '__main__':
    main()
