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)
a=[0]*n
for i in range(n):
    if s[i]=='(':
        l.append(i)
    else:
        if l!=[]:
            a[l[-1]]=i-l[-1]+1
            l.pop(-1)
m=0
i=0
while i<n:
    if a[i]!=0:
        p=0
        while i<n:
            p+=a[i]
            if i+a[i]<n and a[i+a[i]]!=0:
                i+=a[i]
                continue
            break
        if p==m:
            c+=1
        if p>m:
            m=p
            c=1
    i+=1
if m==0:
    print(0,1)
else:
    print(m,c)