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>.
a = input()
n = len(a)
dp=[0]*(n+1)
stack =[]
for i in range(1,n+1):
  if a[i-1]=='(' and stack:
    dp[i]=dp[i-1]
    stack.append(1)
  elif a[i-1]=='(':
    stack.append(1)
    continue
  elif a[i-1]==')' and stack:
    dp[i]=dp[i-1]+1
    stack.pop()

length=0
count =0
for i in range(n+1):
  if dp[i]>length:
    count=1
    length =dp[i]
  elif dp[i]>=length and dp[i]>=1:
    count+=1
if length==0:
  print(length,1)
else:
  print(2*length,count)