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()
a=a[a.find('('):len(a)-a[::-1].find(')')]
n=len(a)
b=[-1]*n
c=[]
d=0
for i in range(n):
    if a[i]=='(':
        c.append(i)
        d+=1
    else:
        if d:
            b[i]=c.pop()
            b[b[i]]=i
            d-=1
l=0
for i in range(n):
    if a[i]=='(' and b[i]!=-1:
        l=max(l,b[i]-i+1)
e=0
for i in range(n):
    if a[i]=='(' and b[i]-i+1==l:
        e+=1
if l:
    print(l,e)
else:
    print(0,1)