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>.
from collections import Counter
s = input()
left = right = 0
maxlength = 0
maxtime = 1
for i in s:
    if i == '(':
        left += 1
    else:
        right += 1
        if right > left:
            right = left = 0
    if left == right and left != 0:
        if left * 2 > maxlength:
            maxlength = left * 2
            maxtime = 1
        elif left * 2 == maxlength:
            maxtime += 1
print(maxlength, maxtime)