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().strip()
open_bracket = longest = temp_longest =0
count = 1
for i in s:
    if i == '(':
        open_bracket += 1
        temp_longest += 1
    else:
        open_bracket -= 1
        if open_bracket == 0:
            temp_longest += 1
            if temp_longest == longest:
                count += 1
            elif temp_longest > longest:
                longest = temp_longest
                count = 1
            open_bracket = 0
            temp_longest = 0
        elif open_bracket > 0:
            temp_longest += 1
        elif open_bracket < 0:
            open_bracket = 0
print(longest)
print('{} {}'.format(longest, count))
