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 = input()

dq = deque()
dq.append(-1)

count = 1
max_len = 0

for i in range(len(s)):

    if s[i] == '(':
        dq.append(i)
     
    else:
        if dq:
            dq.pop()

        if dq:
            if i - dq[-1] == max_len:
                count += 1
            max_len = max(max_len,
                        i - dq[-1])
            
        else:
            dq.append(i)
            
print(max_len, count)
   	     	       			 	 				  		