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 PYTHON3):

Solution:
import sys
input=lambda:sys.stdin.readline().strip()

s=input()
stack=[]
m = 0
ans = 1
xx = -1
for i in range(len(s)):
	if s[i] == '(':stack.append(i)
	else:
		if len(stack) > 0:
			stack.pop()
			optimal = i - stack[-1] if len(stack) > 0 else i - xx
			if optimal >= m:
				if optimal > m: m, ans = optimal, 1
				else: ans += 1
		else:
			xx = i
print(m, ans)