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:
def solve(s):
	l=[]
	length=ref=0
	count=1
	pos=-1
	for i in range(len(s)):
		if s[i]=="(":
			l.append(i)
		elif l:
			l.pop()
			ref=i-l[-1] if l else i-pos
			if ref>length:
				length=ref
				count=1
			elif ref==length:
				count+=1
		else:
			pos=i
	print(length,count)
			
			
			
s=input()
solve(s)