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()
mal,k,lis=0,0,[-1]
for i in range(len(s)):
  if(s[i]=='('):
    lis.append(i)
  elif(len(s)>1):
    lis.pop()
    x=i-lis[-1]
    if(mal<x):
      mal,k=x,1
    elif(mal==x):
      k+=1
print(mal,k)