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
    for i in range(len(s)):
        if s[i] == '(':
            stack = 1
            for j in range(i + 1, len(s)):
                if s[j] == '(':
                    stack += 1
                elif s[j] == ')':
                    stack -= 1
                if stack == -1:
                    seq_len = j - i
                    if seq_len > max_len:
                        max_len, occurence = seq_len, 1
                    elif seq_len == max_len:
                        occurence += 1
                    break
                elif j == len(s) - 1 and stack == 0:
                    seq_len = j - i + 1
                    if seq_len > max_len:
                        max_len, occurence = seq_len, 1
                    elif seq_len == max_len:
                        occurence += 1
                    break

    print(max_len, occurence)

if __name__ == "__main__":
    main()