Problem: 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.

Input

The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.

Output

Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".

Examples

Input

)((())))(()())


Output

6 2


Input

))(


Output

0 1

Solution (in PYTHON3):

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