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>.
lst = []
_max = []
m = 0

for i in input():
    if i == '(':
        lst.append(i)
    elif i == ')' and len(lst) > 0 and lst[-1] == '(':
        m += 2
        lst.pop()
    else:
        _max.append(m)
        m = 0

_max.append(m)

if max(_max) > 0:
    print(max(_max), _max.count(max(_max)))
else:
    print('0 1')
