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>.
brackets = list(input())
current_score = 0
sequence_counter = 0
substring = 0
longest_substring = []
flag = True
for bracket in brackets:
    if bracket == ')' and sequence_counter >= 0:
        sequence_counter -= 1
        current_score += 1
    elif bracket == '(':
        sequence_counter += 1
        current_score += 1

    if sequence_counter < 0:
        flag = False
        longest_substring.append(current_score)
        sequence_counter = 0
        current_score = 0
        substring += 1
x = len(brackets)
if flag:
    print(str(x) + " 1")
else:
    if substring == 0:
        print('0 ' + '1')
    else:
        print(str(max(longest_substring)) + " " + str(substring))
