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())
ans = 0 
le = 0  
st = deque() 
temp = 0

for i in range (len(s)): 
    if s[i] == '(': 
        st.append('(')
    else: 
        if st: 
            st.pop()  
            temp += 2
        else:
            if temp > ans : 
                ans = temp 
                le = 1 

            elif temp == ans : 
                le += 1 
            temp = 0
if temp > ans : 
    ans = temp 
    le = 1 
elif temp == ans : 
    le += 1 
if ans : 
    print(ans , le) 
else:
    print(0 , 1)
