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
# sys.stdin=open("input.txt",'r')
# sys.stdout=open('output.txt','w')
s=input()
open=0
close=0
seen=[0]*(len(s)+2)

for i in range(len(s)):
    if s[i]=='(':
        open+=1
        seen[i+2]
    if s[i]==')' and open>0:
        open-=1
        seen[i+2]=max(seen[i]+2,seen[i+1]+2)
    elif s[i]==')':
        continue
        
    if open==0:
        seen[i+2]=max(seen[i]+2,seen[i+1]+2)
mx=max(seen)
if mx==0:
    print(0,1)
    exit(0)
print(mx,seen.count(mx))

    