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>.
text = input()
l = []
ans = [False] * len(text)
for i in range(len(text)):
	s = text[i]
	if s == "(":
		l.append(i)
	else:
		if l:
			ans[l[-1]], ans[i] = True, True
			l.pop()
counter = 0
max_ = 0
colvo = 0
=for j in range(len(text)):
	if ans[j]:
		counter += 1
	else:
		if counter == max_:
			colvo += 1
		elif counter > max_:
			colvo = 1
			max_ = counter
		counter = 0
if counter == max_:
	colvo += 1
elif counter > max_:
	colvo = 1
	max_ = counter
if max_ == 0:
	print(0, 1)
else:
	print(max_, colvo)