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:
line = input().strip()

d, c = [-1 for char in line], [-1 for char in line]

stack = []

for i, char in enumerate(line):
	if char == '(':
		stack.append(i)
	else:  # if char == ')':
		if not stack:
			c[i] = -1
			d[i] = -1
		else:  # if stack:
			d[i] = stack.pop()
			if line[d[i] - 1] == ')' and c[d[i] - 1] != -1:
				c[i] = c[d[i] - 1]
			else:
				c[i] = d[i]

# print(f'c={c};d={d}')

max_length = max(_ - c[_] if c[_] != -1 else -1 for _ in range(len(line)))

count_max = sum(1 if _ - c[_] == max_length and c[_] != -1 else 0 for _ in range(len(line)))

if max_length == -1:
	print('0 1')
else:
	print(max_length + 1, count_max)