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:
def solve(s):
	end = len(s)
	while end > 0 and s[end-1] == '(':
		end -= 1
	beg = 0
	while beg < end and s[beg] == ')':
		beg += 1
	d = {}
	maxLen, maxCount = 0, 1
	p = 0
	cut = True
	for i in range(beg, end):
		if s[i] == '(':
			if cut:
				d[p] = i
			cut = True
			p += 1
		else:
			if p == 0:
				cut = True
				continue
			cut = False
			p -= 1
			w = i-d[p]+1
			if w > maxLen:
				maxLen = w
				maxCount = 1
			elif w == maxLen:
				maxCount += 1
	return str(maxLen)+' '+str(maxCount)
	
s = raw_input()
print(solve(s))