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>.
st = input()
a = 0
b = 0
l = 0
cnt = 0
for i in st:
   if i=='(':
      cnt+=1
   else:
      cnt-=1
   if cnt==0 and l>0:
      if l>a:
         a=l
         b=1
      elif l==a:
         b+=1
   elif cnt<0:
      cnt=0
      l=0
   else:
      l+=1
if a:
   a+=1
if not b:
   b=1
print(str(a)," "+str(b))