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
import heapq    


def main():
    m,b,s = 0,1,[-1]
    temp = input()
    for i,c in enumerate(temp):
        if c =="(":s.append(i)
        elif len(s)>1:
            s.pop()
            n = i-s[-1]
            if n > m: m,b = n,1
            elif m == n: b+=1
        else:s[0]= i
            
    print(" ".join([str(m),str(b)]))

if __name__ == "__main__":
    main()