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:
s=input()
stack=[]
high_length=0
ss_count=1
for i in range(0,len(s)):
	if(s[i]=='('):
		stack.append(i)
	else:
		if(stack!=[] and s[stack[-1]]=='('):
			stack.pop()
			if(stack!=[]):length=i-stack[-1]
			else:length=i+1
			if(high_length<length):
				high_length=length
				ss_count=1
			elif(high_length==length):
				ss_count+=1
		else:
			stack.append(i)
print(high_length,ss_count)