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]
for starting_i in range(n):
    bracket_sum=0
    bracket_len=0
    valid_bracket=[0]
    for char in string[starting_i:]:
        if char=='(':
            bracket_sum+=1
        else:
            bracket_sum-=1
        if bracket_sum>=0:
            bracket_len+=1
        if bracket_sum==0:
            valid_bracket.append(bracket_len)
        elif bracket_sum<0 :
            break
    brackets.append(max(valid_bracket))


m=max(brackets)
if m==0:
    print(0,1)
else:
    print(m,brackets.count(m))
            
            
        
    
