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
import threading
# import sys
def ri(): return int(input())
def rs(): return input()
def rl(): return list(map(int, input().split()))
def rls(): return list(input().split())


# threading.stack_size(10**8)
# sys.setrecursionlimit(10**6)


def main():
    # sol first code later dorime
    s = list(rs())
    n = len(s)
    c = [False]*n
    st = []
    for idx, i in enumerate(s):
        if i == '(':
            st.append(idx)
        else:
            if st:
                c[st.pop(-1)] = True
                c[idx] = True
    h = ''
    mxh = ''
    cs = 1
    for idx, i in enumerate(c):
        if i:
            h += s[idx]
            if len(h) > len(mxh):
                mxh = h
                cs = 1
            elif len(h) == len(mxh):
                cs += 1
        else:
            h = ''
    if mxh == '':
        print(0, 1)
    else:
        print(len(mxh), cs)
    pass


main()
# threading.Thread(target=main).start()
