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>.
st = [-1]
Max = Count = 0
for i, c in enumerate(input()):
	if c == '(':
		st.append(i)
	else:
		if len(st) > 1:
			st.pop()
			temp = i - st[-1]
			if temp > Max:
				Max = temp
				Count = 1
			elif temp == Max:
				Count += 1
		else:
			st[0] = i
if Max:
	print(Max, Count)
else:
	print(0, 1)