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()
str=[-1]
tot=1
ans=0
for i in range(len(s)):
    if s[i]=='(':
        str.append(i)
    else:
        str.pop()
        if len(str)>0:
            res=i-str[-1]
            if res>ans:
                ans=res
                tot=1
            elif res==ans:
                tot+=1
        else:
            str.append(i)
print(ans,tot)
     		    