Problem: 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.

Input

The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.

Output

Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".

Examples

Input

)((())))(()())


Output

6 2


Input

))(


Output

0 1

Solution (in PYTHON3):

Solution:
seq = input()

longest = 0
total = 0

st = [-1]

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

st.append(len(seq))

#print(st)


if len(st) > 0:
#  prev = st[0]
  longest = st[0]
#  if st[0] == len(seq):
#    total = 1

#longest = 0
#total = 0

m = {}

#print(longest)

for i in range(1, len(st)):
  if st[i-1] + 1 != st[i]:
    length = st[i] - st[i-1] - 1
    longest = max(longest, length)
    if length not in m:
      m[length] = 1
    else:
      m[length] += 1
#    print(st[i] - st[i-1] - 1)
#    total += 1

#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, m[longest])
else:
  print(0, 1)