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 find_longest_regular_bracket_sequence(s):
    stack = []
    max_len = 0
    count = 0

    stack.append(-1)

    for i in range(len(s)):
        if s[i] == "(":
            stack.append(i)
        else:
            stack.pop()
            if stack:
                length = i - stack[-1]
                if length > max_len:
                    max_len = length
                    count = 1
                elif length == max_len:
                    count += 1
            else:
                stack.append(i)

    if max_len == 0:
        return (0, 1)
    return (max_len, count)

def main():
    s = input()
    result = find_longest_regular_bracket_sequence(s)
    print(result[0], result[1])

if __name__ == "__main__":
    main()
        