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 main():
	s = raw_input()
	n = len(s)
	dp = [0] * n
	st = []
	maxLen, cnt = 0, 1
	for i, c in enumerate(s):
		if '(' == c: st.append(i)
		else:
			if len(st) > 0:
				left = st[-1]
				del st[-1]
				dp[i] = i - left + 1 + dp[left - 1] if left > 0 else i - left + 1
				if dp[i] > maxLen:
					maxLen = dp[i]
					cnt = 1
				elif dp[i] == maxLen: cnt += 1
	print maxLen, cnt
 
if __name__ == "__main__": main()