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()
countParantheses = 0
current = 0
result = 0
started = True
count = 0

for s in S + 'q':
    if s == '(':
        countParantheses += 1
    elif s == ')' and countParantheses > 0:
        countParantheses -= 1
        current += 1
        started = True
        result = max(result, current)
    else:
        current = 0
        if started:
            count += 1
        started = False

print(result * 2, count)
