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:
string=input()
def main(string):
	st=[]
	answer=[False]*(len(string)+1)
	for i in range(0,len(string)):
		if string[i]=="(":
			st.append(i)
		else:
			if not st:
				continue
			answer[st.pop()] = True
			answer[i] = True
	res = []
	mx = 0
	for i in range(0,len(answer)):
		if answer[i]==False:
			res.append(mx)
			mx=0
			continue
		mx+=1

	mx = max(res)
	if mx==0:
		print(0, 1)
	else:
		print(mx, res.count(mx))
main(string)