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>.
# @author: guoyc
# @date: 2018/7/20

s = input()

ml = 0
cnt = 1

t = 0
st = 0
for i, c in enumerate(s):
    if c == '(':
        if t == 0:
            st = i
        t += 1
    elif c == ')':
        t -= 1
        if t == 0:
            ll = i - st + 1
            if ll > ml:
                ml = ll
                cnt = 1
            elif ll == ml:
                cnt += 1
        if t < 0:
            t = 0

print(ml, cnt)
