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>.
import collections


s = input()

stack = []
length = 0
result = collections.defaultdict(int)

for w in s:
    # print(w, stack)
    # print(length)
    if stack and (stack[-1] == '(' and w == ')'):
        length += 2
        result[length] += 1
        stack.pop()
        continue
    stack.append(w)
    if not stack or stack[-1] == ')':
        length = 0

max_length = max(result.keys())
if not max_length:
    print('0 1')
else:
    print('{} {}'.format(max_length, result[max_length]))