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:
c = r = p = 0
d = [(0, -1)]
for i, x in enumerate(raw_input()):
	c += [-1, 1][x == '(']
	while d and d[-1][0] > c:
		d.pop()
	if d and d[-1][0] == c:
		t = i - d[-1][1]
		if r < t:
			r, p = t, 1
		elif r == t:
			p += 1
	else:
		d.append((c, i))
print r, [1, p][r > 0]