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()
l=[]
n=len(s)
p=0
c=0
for i in range(n):
    if s[i]=='(':
        p=p+1
    if s[i]==')':
        p=p-1
        if p>0:
            c=c+1
        if p==0:
            l.append(c)
            c=0
        elif p<0:
            l.append(c)
            c=0
            p=0
if p>0:
    l.append(c-p)
l.sort()
m1,m2=max(l),l.count(max(l))
print(m1,m2)