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
    last_end = -1
    for i in range(len(s)):
        if s[i] == "(":
            stack += 1
        else:
            stack -= 1
        if not stack:
            if i - last_end > max_len:
                max_len, occurence = i - last_end, 1
            elif i - last_end == max_len:
                occurence += 1
            last_end = i
        if stack == -1:
            stack = 0
            last_end = i
    print(max_len, occurence)

if __name__ == "__main__":
    main()