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 defaultdict

d = defaultdict(int)
s = list(input())

count = 0
balance = 0
for c in s:
    balance += 1 if(c == "(") else -1
    if(balance == -1):
        if(count > 0):
            d[count] += 1
            count = 0
        balance = 0
    else:
        count += 1
if(count > 0):
    d[count] += 1

d = dict(d)
if(d):
    key = max(list(d.keys()))
    print("%d %d" % (key, d[key])) 
else:
    print("0 1")