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>.
string=input()

n=len(string)
brackets=[0]
bracket_sum=0
bracket_len=0
for char in string:
    if char=='(':
        bracket_sum+=1
    else:
        bracket_sum-=1
    if bracket_sum>=0:
        bracket_len+=1
    if bracket_sum==0:
        brackets.append(bracket_len)
    elif bracket_sum<0 :
        bracket_sum=0
        bracket_len=0
m=max(brackets)
print(m,brackets.count(m))
            
            
        
    
