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 sys

input = sys.stdin.readline
a=input().strip('\n')

m =[]
stack = []
for i in range(len(a)):
    if a[i] == "(":
        stack.append(i)
    else:
        if len(stack) > 0:
            start = stack.pop()
            m.append(len(a[start:i+1]))
if m:
    maxs = max(m)
    print(maxs, m.count(maxs))
else:
    print(0, 1)