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

seq = list(input())
stack = []
count = 0
ans = defaultdict(int)
for i in range(len(seq)):
    if seq[i] == "(":
        stack.append(i)
    if seq[i] == ")":
        if len(stack) and seq[stack[-1]] == "(":
            stack.pop()
            count +=2
            
            if len(stack) == 0:
                ans[count] += 1
                count = 0
                
if len(ans) == 0:
    print(0,1)
else:
    print(max(ans), ans[max(ans)])     