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()
ans=0
from collections import defaultdict
d=defaultdict(lambda:0)
stack=[]
temp=0
for i in s:
    if i=="(":
        stack.append("(")
    else:
        if stack:
            temp+=2
            stack.pop()
            d[temp]+=1
            ans=max(ans,temp)
            if len(stack)==0:
                temp=0
        else:
            temp=0
if ans==0:
    print(0,1)
else:
    print(ans,d[ans])
