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>.
l=input()
c=0
maxi=0
s=[]
d=0
for i in range(len(l)):
    if l[i]=='(' :
        s.append(i)
    elif s:
        s.pop()
        c+=2
    if not s:
        if maxi==c:
            d+=1
        elif maxi<c:
            d=1
            maxi=c
        c=0
    
if maxi==0:
    print(0,1)
else:
    print(maxi,d)