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>.
n = input()
counter = dict()

stack = []
curr = 0
for char in n:
  if char == ')' and not stack:
    continue
  if char == '(':
    stack.append(char)
  else:
    stack.pop()
    curr += 2
    if curr not in counter:
      counter[curr] = 0
    counter[curr] += 1 
    if not stack:
      curr = 0

if not counter:
  print(0, 1)
else:
  maxLength = max(counter.keys())
  print(maxLength, counter[maxLength])