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()
w,c,b,l=0,1,-1,[]
for i in range(len(s)):
   if s[i]=='(':l.append(i)
   elif l:
      l.pop()
      t=i-l[-1] if l else i-b
      if t>w: w,c=t,1
      elif t==w: c+=1
   else:b=i
print(w,c)