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:
import sys
buff=raw_input()
tmp=ans=ret=0
pre=-1
cnt=1
stack=[]
for i in xrange(len(buff)):
	if buff[i]=='(':
		stack.append(i)
	elif stack:
		stack.pop()
		if stack:
			det=i-stack[-1]
		else:
			det=i-pre
		if det>ans:
			ans=det
			cnt=1
		elif det==ans:
			cnt+=1
	else:
		pre=i
print ans,cnt