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()
max_len = 0
count = 1

current_len = 0

for i in range(len(s)):
    if s[i] == ')':
        if dq:
            current_len += 2

            if current_len == max_len:
                count += 1
            elif current_len > max_len:
                max_len = current_len
                count = 1

            dq.pop()
        else:
            current_len = 0

    else:
        if dq:
            dq.append(s[i])
        else:
            current_len = 0
            dq.append(s[i])

print(current_len, count)
  	   	  								    		 	 	 		