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)
stack =[]

for i in range(n):
  if a[i]=='(':
    stack.append(i)
    continue
  if not stack:
    continue

  j = stack.pop()
  dp[i]=i-j+1+(dp[j-1] if j>1 else 0)
ans =0
length = max(dp)
count = dp.count(length)
if length==0:
  print(length,1)
else:
  print(length,count)
