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>.
seq = input()
st = []
currentSize = 0
maxSize = 0
amount = 0
for c in seq:
  if c == ")" and len(st)>0:
    currentSize += 2 + st.pop()
  else:
    if c == "(":
      st.append(currentSize)
    if currentSize>maxSize:
      maxSize = currentSize
      amount = 1
    elif currentSize==maxSize:
      amount += 1
    currentSize = 0
if currentSize>maxSize:
  maxSize = currentSize
  amount = 1
elif currentSize==maxSize:
  amount += 1
if maxSize == 0:
  amount = 1
print(maxSize,amount)