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>.
seq = input()
st = []
currentSize = 0
maxSize = 0
amount = 0
for c in seq:
	if c == "(":
		st.append(c)
	elif len(st)==0:
		if currentSize>maxSize:
			maxSize = currentSize
			amount = 1
		elif currentSize==maxSize:
			amount += 1
		currentSize = 0
	else:
		st.pop()
		currentSize += 2
if currentSize>maxSize:
	maxSize = currentSize
	amount = 1
elif currentSize==maxSize:
	amount += 1
if maxSize == 0:
	amount = 1
print(maxSize,amount)