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 = str(input())

longest = 0
total = 0

st = []

for i in range(len(seq)):
  ch = seq[i]
#  if len(st) == 0:
#    st.append(i)
  if ch == ')':
    if len(st) > 0 and seq[st[-1]] == '(':
       st.pop()
    else:
       st.append(i)
  else:
    st.append(i)

st.append(len(seq))

#print(st)

total = len(st) - 1

if len(st) > 0:
  prev = st[0]

for i in range(1, len(st)):
#   print(i, prev, st[i])
   longest = max(longest, st[i] - prev - 1)
   prev = st[i]

if longest != 0:
   print(longest, total)
else:
  print(0, 1)
