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()
score=0
count=1
maxa=0
from collections import defaultdict
al=defaultdict(list)
al[0].append(0)
for i in range(len(s)):
    if(s[i]=='('):
        score+=1
        al[score].append(i)
    else:
        if(score>0):
            if(i-al[score][-1]+1>maxa):
                maxa=i-al[score][-1]+1
                count=1
            elif(i-al[score][-1]+1==maxa):
                count+=1
            score-=1

if(score==0):
    print(len(s),1)
    exit()
if(maxa==0):
    print(0,1)
else:
    print(maxa,count)
                
            




            
            
