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>.
n = list(input())
stack_b = [0]
length = 0
lenarray = [0]
counter = 0

for i in range(len(n)):
    if n[i] == "(":
        stack_b.append(i + 1)
    else:
        if len(stack_b) > 1:
            stack_b.pop()
            length = i + 1 - stack_b[-1]
            if max(lenarray) < length:
                lenarray = [0]
                lenarray[0] = length
            elif max(lenarray) == length:
                lenarray.append(length)
        else:
            stack_b.append(i + 1)

print(max(lenarray), len(lenarray))