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)
    dp = [0]*n
    st = []
    for idx, i in enumerate(s):
        if i == '(':
            st.append(idx)
        else:
            if st:
                b = st.pop()
                dp[idx] = dp[b-1]+(idx-b+1)
    mx = max(dp)
    if mx == 0:
        print(0, 1)
    else:
        print(mx, dp.count(mx))
    pass


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