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:
if __name__ == "__main__":
	tmp = str(input())
	local_start = None
	local_max = 0
	how_many = 1
	lst = [-1]
	for i in range(len(tmp)):
		
		if tmp[i]=="(":

			lst.append(i)
		elif len(lst)>1:
			x = lst.pop()
			qq = i -lst[-1]

			if qq==local_max:
				how_many+=1
			elif qq>=local_max:
				local_max=qq
				how_many=1
		else:
			lst[0]=i
	
		
			
	print(local_max,how_many)