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>.
import sys
rln=sys.stdin.buffer.readline
rl=lambda:rln().rstrip(b'\r\n').rstrip(b'\n')
ri=lambda:int(rln())
rif=lambda:[*map(int,rln().split())]
rt=lambda:rl().decode()
rtf=lambda:rln().decode().split()
inf=float('inf')
dir4=[(-1,0),(0,1),(1,0),(0,-1)]
dir8=[(-1,-1),(0,-1),(1,-1),(-1,0),(1,0),(-1,1),(0,1),(1,1)]
YES,NO,Yes,No,yes,no='YES','NO','Yes','No','yes','no'

s=rt()
n=len(s)
mx,cnt=0,1
stk=[-1]
for i in range(n):
  if s[i]=='(':
    stk.append(i)
  else:
    stk.pop()
    if not stk:
      stk.append(i)
    else:
      l=i-stk[-1]
      if mx==l:
        cnt+=1
      elif mx<l:
        mx,cnt=l,1

print(mx,cnt)
