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()
s1=0
s2=0
ans=[]
for i in s:
    if(i=='('):
        s1+=1
    elif(i==')'):
        s2+=1
    if(s1==s2):
        ans.append(s1+s2)
    if(s1<s2):
        s1=0
        s2=0
if(ans==[]):
    print(0,1)
else:
    ma=max(ans)
    print(ma,ans.count(ma))
