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>.
def f(s):
    k=0
    c=0
    l=[]
    for a in s:
        if a=="(":
            k+=1
        else:
            #l.append(2*k)
            k-=1
        
        if k>=0:
            c+=1
        else:
            l.append(c)
            k,c=0,0
    if c!=0:
        l.append(c)
    z=max(l)
    d={}
    if z!=0:
        for a in l:
            if a in d.keys():
                d[a]+=1
            else:
                d[a]=1
        
        print(z,d[z])
        #print(l,d)
    else:
        print("0 1")

f(input())