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()+')'
n=len(s)
stack=[]
lenth=0
count=0
start=0
templen=0
for i,c in enumerate(s):
    if c=='(':
        stack.append(i)
        start=1
    else:
        if len(stack)==0:
            if start==1:
                start=0
            lenth=max(lenth,templen)
            templen=0
            count+=1
        else:
            templen+=2
            stack.pop()
            
lenth=max(templen,lenth)
if lenth==0:
    count=1
print(lenth,count)            
            
    