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>.
li = list(input())
count = height = 0
countHeight = 0
stack = 0

for i in li :
    if i == "(" :
        stack += 1
    else :
        if stack > 0 : 
            count += 1
            stack -= 1
        else :
            if count > height :
                height = count
                countHeight = 1
            elif count == height and count != 0 :
                countHeight += 1
            count = 0
            stack = 0
if count > height : countHeight = 1
elif count == height : countHeight += 1
exit(print(height * 2 , countHeight))