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()
    s = s.lstrip(')')
    s = s.rstrip('(')

    i = 0
    short_seq = []
    while i < 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 == 0:
                        short_seq.append((i, j))
                        i = j
                        break
        i += 1

    max_len, occurence = 0, 1
    i = 0
    while i < len(short_seq):
        start_index = short_seq[i][0]
        while i < len(short_seq) - 1 and short_seq[i][1] + 1 == short_seq[i + 1][0]:
            i += 1
        seq_len = short_seq[i][1] - start_index + 1
        if seq_len > max_len:
            max_len, occurence = seq_len, 1
        elif seq_len == max_len:
            occurence += 1
        i += 1

    print(max_len, occurence)

if __name__ == "__main__":
    main()