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>.
from collections import deque
s= deque()
nb1=0
nb2=0
c=0
for i in input():
  if s and i==')' and (s[-1]=='('):
    s.pop()
    nb1+=1
    nb2= True
  else:
    s.append(i)
    if nb2: c+=1
    nb2= False
if nb1==0:print(0,'',1)
else:print(nb1,c)
