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.
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 10<sup class="upper-index">6</sup>.
s=input()
i=0
para=0
mx=0
d=0
times=1
while i<len(s):
	if s[i]=="(":
		para+=1
	else:
		if para==1:
			if d==mx-1:
				times+=1
			elif d>mx-1:
				mx=d+1
				times=1
			d=0	
			para = 0
		elif para>1:
			d+=1
			para-=1
	i+=1
print(mx*2,times)