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 = input()

opened, closed = 0, 0
max_length_substring = 0
valid_index, index = 1, 1
for c in s:
    if c == ')' and opened == 0:
        index += 1
        continue
    if c == '(':
        if closed == 0: opened += 1
        else:
            opened, closed = 0, 0
            continue
    else: closed += 1
    if opened == closed:
        max_length_substring = max(max_length_substring, opened + closed)
        valid_index = index
        opened, closed = 0, 0
print(max_length_substring, valid_index)