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:
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)