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()

p = []
p.append(-1)
lls = 0
occ = 1
for i in range(len(s)) :
  if s[i] == '(' :
    p.append(i)
  elif len(p) > 1 :
    
    p.pop()
    n = i - p[-1]
    if n > lls :
      lls = n
      occ = 1
    elif n == lls :
      occ+=1
  else :
    p[0] = i

print(lls, occ)