Problem: 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.

Input

The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.

Output

Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".

Examples

Input

)((())))(()())


Output

6 2


Input

))(


Output

0 1

Solution (in PYTHON):

Solution:
s = raw_input()
ds = range(len(s))

a1 = 0
a2 = 1
p = []
i = 0
for x in s:
	ds[i] = False
	i += 1
	if x == '(':
		p.append(i)
	else:
		if len(p) == 0:
			continue
		y = p.pop()
		ds[y-1] = ds[i-1] = True
i = 0
y = 0
for x in s:
	i += 1
	if ds[i-1] == False:
		y = 0
		continue
	y += 1
	if y > a1:
		a1 = y
		a2 = 1
	elif y == a1:
		a2 += 1
print a1, a2