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()
stack = []
max_length = 0
length = 0
ans = 0
f = 0
for idx, i in enumerate(s):
    if i == "(":
        stack.append(idx)
    else:
        if stack:
            x = stack.pop()
            length = idx - x + 1
            if length == max_length:
                f += 1
            else:
                max_length = max(max_length, length)
                f = 1
if max_length == 0:
    print("0 1")
else:
    print(max_length, f)
            