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():
    longest = 0
    count = 1
    head = tail = 0
    for cursor, paren in enumerate(input()):
        if paren == "(":
            head += 1
        elif head == 0:
            tail = 0
        else:
            head -= 1
            tail += 2
            if tail == longest:
                count += 1
            elif tail > longest:
                longest = tail
                count = 1
    print(longest, count)


if __name__ == '__main__':
    main()
