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>.
line = input()

maxLength = 0
n = 1
brackets = 0 
length = 0
for b in line:
    if b == "(":
        brackets += 1
    else:
        brackets -= 1
    
    if brackets >= 0:
        length += 1
    if brackets <= 0:
        if length > maxLength:
            maxLength = length
            n = 1
        elif length == maxLength:
            n += 1
        length = 0

    brackets = max(brackets, 0)

print(str(maxLength) + " " + str(1 if maxLength == 0 else n))