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