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>.
def main():
    s = input()
    max_len, occurence = 0, 1
    stack = 0
    for i in range(len(s)):
        if s[i] == '(':
            if stack < 0 or not i:
                start = i
                stack = 0
            stack += 1
        else:
            stack -= 1
            if not stack and (i == len(s) - 1 or s[i + 1] == ')'):
                seq_len = i - start + 1
                if seq_len > max_len:
                    max_len, occurence = seq_len, 1
                elif seq_len == max_len:
                    occurence += 1

    print(max_len, occurence)

if __name__ == "__main__":
    main()