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>.
brk = input()

cnt = 0
lng = 0
acc = 0
crr = 0

for k in range(len(brk)):
	if brk[k] == '(':
		acc += 1
	else:
		acc -= 1

	if acc < 0:
		if crr > 1:
			cnt += 1
			if crr > lng:
				lng = crr

		crr = 0
		acc = 0		
	else:
		crr += 1

if crr > 1:
	cnt += 1
	if crr > lng:
		lng = crr

if lng == 0:
	cnt = 1

print(lng, cnt)
