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>.
from collections import deque
string = input()
stack = deque()
S = [-1]*100001
E = [-1]*100001
F = [0]*100001
ans = 0
for i, s in enumerate(string):
    if s == '(':
        stack.append(i)
    else:
        if len(stack) == 0:
            S[i] = E[i] = -1
        else:
            idx = stack.pop()
            S[i] = E[i] = idx
            if string[idx-1]==")" and idx>0 and S[idx-1]>=0:
                E[i] = E[idx-1]
            l = i-E[i]+1
            F[l]+=1
            ans = max(ans, l)
F[0] = 1
print(ans, F[ans])
