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()
a,b,st=0,1,[-1]
for i,l in enumerate(s):
    if l=='(':
        st.append(i)
    elif len(st)>1:
        st.pop()
        n=i-st[-1]
        if a<n:
            a,b=n,1
        elif a==n:
            b+=1
    else:
        st.append(i)
print(a,b)