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()+'*'
arr = deque()
m = 0
count = 0
m_count = 1
for skob in s:
    if (len(arr)>0 and arr[-1] == ')') or skob == '*':
        if count>0:
            if count>m:
                m = count
                m_count = 0
                m_count += 1
            elif count == m:
                m_count += 1
        count = 0
    if skob == '(':
        arr.append('(')
    elif skob == ')':
        if len(arr)>0 and arr[-1] == '(':
            arr.pop()
            count += 2
        else:
            arr.append(')')

print(m,m_count)