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>.
in_str = input().strip()
stack = []
max_len = 0
counter = 0
inc = 0
for each in in_str:
    if each == ")" and len(stack)==0:
        pass
    elif each ==")" and len(stack)>0 :
        stack.pop()
        counter = counter + 2
    else:
        stack.append(each)
        
    if len(stack) == 0:
        if(counter == max_len):
            inc = inc + 1
        max_len = max(max_len,counter)
        counter = 0
if max_len == 0:
    print(max_len," 1")
else:
    print(max_len," ",inc)