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>.
# -*- coding: utf-8 -*-
"""
Created on Fri Dec 30 11:40:40 2022

@author: rohan
"""

b = input()
s = []
maxm = 0
count = 0
for i in range(len(b)):
    if b[i] == "(":
        s.append(i)
    else:
        if s:
            top = s.pop()
            if (i - top + 1) > maxm:
                maxm = i - top + 1
                count = 1
            elif (i - top + 1) == maxm:
                count += 1

if maxm == 0 and count == 0:
    print("0 1")
else:
    print(str(maxm) + " " + str(count))