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>.
s = str(input())

mx_len = 0
count = 0

b = 0
buf_correct = 0
buf_search = 0

for i in s:
    if i == ")":
        b -= 1
        buf_search += 1
    else:
        b += 1
        buf_search += 1

    if b < 0:
        buf_correct = 0
        buf_search = 0
        b = 0
    elif b == 0:
        buf_correct += buf_search
        buf_search = 0
        if buf_correct > mx_len:
            mx_len = buf_correct
            count = 1
        elif buf_correct == mx_len:
            count += 1

if mx_len == 0:
    print(0, 1)
else:
    print(mx_len, count)
