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()

a, b = [], []

for i, x in enumerate(s):
    if x == '(':
        b.append(i)
    elif b:
        j = b.pop()
        
        while a and a[-1][0] > j:
            a.pop()
        
        if a and a[-1][1] == j - 1:
            a.append((a.pop()[0], i))
        else:
            a.append((j, i))

print(max(x[1] - x[0] + 1 for x in a) if a else 1, len(a))
