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 

s = str(input())
n = len(s) 
ans = 0 
le = 0  
st = deque() 
temp = 0 
op = [-1]*n 
for i in range (len(s)): 
    if s[i] == '(': 
        st.append(i) 
    else: 
        if st : 
            j = st.pop()  
            if j-1 >= 0 : 
                k = op[j-1] 
                if k != -1 : 
                    op[i] = k  
                else:
                    op[i] = j 
            if i - op[i] + 1 > ans : 
                le = 1 
                ans = i- op[i] + 1 
            elif i - op[i] + 1 == ans : 
                le += 1 
if ans > 0 :
    print(ans , le) 
else:
    print(0 , 1)
    