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>.
s = input() + ')'
n = len(s)
Max , MaxIndex = 0 , 0
i = 0
while i < n:
    Sum , left = 0 , 0
    for k in range(i , n):
        if s[k] == ')' :
            if left > 0:
                left -= 1
                Sum += 1
            else:
                if Sum > Max:
                    Max = Sum
                    MaxIndex = i
                i = k+1
                break
        else:
            left += 1
            Sum += 1
    i += 1
print(Max,MaxIndex+1)