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.
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 10<sup class="upper-index">6</sup>.
# Use stack to store opening brackets and expand the regular sequence when a closing bracket is introduced.

a, b, s = 0, 1, [-1]
for i, c in enumerate(raw_input()):
	if c == '(': s.append(i)
	elif len(s) > 1:
	    # Top of the stack pairs with ')'
		s.pop()
		n = i - s[-1]
		if a < n: a, b = n, 1
		elif a == n: b += 1
	else: s[0] = i
print a, b