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()
stack = []
stack.append( ('-', -1) )
max_len = 0
max_count = 1
for x in xrange(len(s)):
	if s[x] == '(':
		stack.append( ('(', x) )
	else:
		if stack[-1][0] == '(':
			stack.pop()
			if x - stack[-1][1] > max_len:
				max_len = x - stack[-1][1]
				max_count = 1
			elif x - stack[-1][1] == max_len:
				max_count += 1
		else:
			stack.append( (')', x) )
print max_len, max_count