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()
stack=[]
length=0
high_length=0
ss_count=1
for i in s:
	if(stack==[] or i=='('):
		stack.append(i)
	else:
		if(stack[-1]=='('):
			stack.pop()
			length+=2
			if(high_length<length):
				high_length=length
				ss_count=1
			elif(high_length==length):ss_count+=1
		else:length=0
print(high_length,ss_count)
