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>.
brackets = input()
longest = 0
count = 0
open = 0
closed = 0
for bracket in brackets:
    if bracket == "(":
        open += 1
    if bracket == ")":
        closed += 1
    if closed > open:
        closed, open = 0, 0
    elif closed == open:
        total = closed+open
        if total == longest:
            count += 1
        elif total > longest:
            longest = total
            count = 1

print(longest, count)