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>.
s = input()

cls = [0] * len(s)
ext = [0] * len(s)
freq = [0] * (len(s) + 1)
freq[0] = 1
maxLen = 0

stack = []
for i in range(len(s)):
  if s[i] == "(":
    stack.append(i)
  else:
    if not stack:
      cls[i] = ext[i] = -1
    else:
      ind = stack.pop()
      cls[i] = ext[i] = ind
      if ind > 0 and s[ind-1] == ")" and cls[ind-1] != -1:
        ext[i] = ext[ind-1]
      l = i - ext[i] + 1
      freq[l] += 1
      maxLen = max(l, maxLen)

print(maxLen, freq[maxLen])