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>.
string, counter, size = input(), 1, 0
for idx1 in range(len(string)):
	valid_counter = 0
	for idx2 in range(idx1, len(string)):
		if string[idx2] == "(":
			valid_counter += 1
		else:
			valid_counter -= 1
		if valid_counter == 0:
			tmp_size = idx2 - idx1 + 1
			if tmp_size > size:
				size, counter = tmp_size, 1
			elif tmp_size == size:
				counter += 1
		if valid_counter < 0:
			break
print(size, counter)
