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>.
string = "))("
l = []
times = 0
sub = 0
for x in string:
    if x == '(':
        l.append(x)
        sub = sub +1
    else:
        try:
            l.remove('(')
            sub = sub +1
            times = times + 1
        except:
            pass
try:
    sub = sub // times
except:
    sub = 1
    
print(times , sub)