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>.
import sys

exp = sys.stdin.readline().strip()

stack = []

num_longest = 0
longest = 0
paired = 0

for symbol in exp:
	if len(stack) > 0 and symbol == ')' and stack[-1] == '(':
		#print('pop')
		stack.pop()
		paired += 1
		#print('paired: {}'.format(paired))
	else:
		if paired > 0:
			if paired * 2 > longest:
				num_longest = 1
				longest = paired * 2
			elif paired * 2 == longest:
				num_longest += 1

		if symbol == ')':
			paired = 0

		stack.append(symbol)
	#print(stack)
			

if paired > 0 and paired * 2 == longest:
	num_longest += 1

if num_longest == 0:
	print('0 1')
else:
	print('{} {}'.format(longest, num_longest))
