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>.
s=input()

r=0
c=0
maxx=0
n=0

for i in range(len(s)):
    if(s[i]==")"):
        r-=1
    else:
        r+=1
    if(r<0):
        r=0
        c=0
    elif(r==0):
        c+=1
        if(c>maxx):
            maxx=c
            n=1
        elif(c==maxx):
            n+=1
    else:
        c+=1

if(maxx==0):
    print("0 1")
else:
    print(maxx,n)
    
