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()
n=len(s)
l=[]
cpt,nb,lng=0,0,0
for i in range(n):
    if s[i]=="(":
        if cpt<0:
            cpt=1
            lng+=1
        else:
            cpt+=1
            lng+=1
    else:
        cpt-=1
        if cpt>=0:
            lng+=1
    if cpt==0:
        l.append(lng)
        lng=0
        nb+=1
if l==[]:
    print("0 1")
else:
    print(max(l),nb)