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()

longest = 0
num = 0

opn = 0
l = 0
for c in s:
	if c == "(":
		opn += 1
		l += 1
	elif c == ")" and opn > 0:
		opn -= 1
		l += 1
		if opn == 0:
			num += 1
			if l > longest:
				longest = l
			l = 0

if opn > 0:
	l -= opn
	if l > 0:
		if l > longest:
			longest = l
		num += 1

if num == 0:
	print(0,1,sep=" ")
else:
	print(longest,num,sep=" ")