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
stk = 0
temp = 0
keep = defaultdict(int)
keep[0]+=1
for i in input():
    if i == "(":
        stk += 1
    else:
        if stk:
            stk -=1
            temp += 1
            keep[temp * 2] += 1
        else:
            temp = 0
ans = max(keep)

print(ans, keep[ans])
