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, v, c = [], 0, 1
for i, ch in enumerate(input()):
    if ch == '(':
        s.append(i)
    elif s:
        x = i - s.pop() + 1
        if x > v:
            v, c = x, 1
        elif x == v:
            c += 1
print(v, c)