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 math


def getList(method=int):
    return list(map(method, input().split()))


def getInt():
    return int(input())


def solve():
    s = input()
    stk = list()
    lcounts = dict()

    for i, v in enumerate(s):
        if v == '(':
            stk.append(i)
        elif v == ')' and stk:
            l = i - stk.pop() + 1
            lcounts[l] = lcounts[l] + 1 if l in lcounts else 1

    if len(lcounts):
        mx = max(lcounts.keys())
        print(mx, lcounts[mx])
    else:
        print(0,1)

solve()
# for _ in range(getInt()):
#     size = getInt()
#     solve(size)
