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 PYTHON):

Solution:
Brackets=raw_input().strip()
Stack,maxs,num=[],0,1
def1=0
p=-1
for i in xrange(len(Brackets)):
	if Brackets[i]=='(':
		Stack.append(i)
	elif Stack:
		cur=Stack.pop()
		def1=i-(Stack[-1] if Stack else p)
		if def1>maxs:
			maxs=def1
			num=1
		elif def1==maxs:
			num+=1
	else:
		p=i
print maxs,num