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>.
a=input()
if "("not in a or ")"not in a:
    print(0,1)
else:
    b=a.find("(")
    d=[]
    s=[a[b]]
    c=1
    a=a[b+1:]
    for i in a:
        if s==[] and c!=0:
            d+=[c]
            c=0
        if i=="(":
            s+=["("]
            c+=1
        else:
            if s==[]:
                c=0
            else:
                k=s.pop(-1)
                if k=="(":
                    c+=1
                else:
                    s=[]
                    c=0
    if s==[] and c!=0:
        d+=[c]
    if d!=[]:
        m=max(d)
        print(m,d.count(m))
    else:
        print(0,1)