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>.
a = input()
open = []
close = []
for i in a:
    if i==')':
        close.append(i)
    elif i=='(':
        open.append(i)
biggest = []
b = 0
if len(open)>len(close):
    b = len(open)-len(close)
elif len(open)<len(close):
    b = len(close)-len(open)
elif len(close)==len(open):
    b = 0
if b!=1:
    print(((len(open)-b)*2)-b, b)
else:
    print(0, 1)