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>.
st = [-1]

ml, cnt = 0, 1

for i, c in enumerate(s):
    if c == '(':
        st.append(i)
    else:
        if len(st) > 1:
            st.pop(-1)
            ll = i - st[-1]
            if ll > ml:
                ml, cnt = ll, 1
            elif ll == ml:
                cnt += 1
        else:
            st[0] = i

print(ml, cnt)