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
from collections import Counter
input = sys.stdin.readline

def main():
    s = input().strip()
    n = len(s)

    stack = []

    ans = [0]
    cur = 0

    for i in range(n):
        if s[i] == "(":
            stack.append(1)
        else:
            if stack:
                stack.pop()
                cur += 2
                ans.append(cur)
            else:
                cur = 0

    m = max(ans)

    if m:
        print(m, ans.count(m))
    else:
        print(0, 1)

main() 


