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>.
string = input().replace(" ","")	
stack = list()
res = 0
stack.append(-1)
count = 0
for index , x  in  enumerate(string):	
	if x == "(":
		stack.append(index)
	else:
		if len(stack) != 0 :
			stack.pop()
			
		#if stack[-1] != ")" and x == ")"
		
		if len(stack) !=0:
			 
			lenx = index - stack[-1]
			if res < lenx:
				res = lenx
				count+=1
			else:
				count=1
			
			
			
			
			
		else:
			stack.append(index)
		
	

print(res, count)