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>.
l = list(input())
counter = 0
number = 1
maximum = 0
stack = []
flag = 0
for i in l:
    if i == "(":
        stack.append(i)
    else:
        if len(stack) != 0:
            stack.pop()
            counter += 1
        else:
            if maximum<counter:
                number = 1
                maximum = counter
            elif maximum == counter and maximum != 0:
                number += 1
            counter = 0

if maximum<counter:
    number = 1
    maximum = counter
elif maximum == counter and maximum != 0:
    number += 1

print(maximum*2,number)

