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>.
stack=[]
maxi=count=0
num=1
for i in input():
    if i == '(':
        stack.append(i)
    else:
        if len(stack)== 0 or stack.pop() != '(':
            maxi=max(maxi,count)
            if count:
                num+=1
            count=0
        else:
            count+=2
maxi=max(maxi,count)
print(maxi,num)
