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>.
ins, maxlen, count, stack=input(), 0, 1, [-1]
for i,c in enumerate(ins):
    if c=='(': 
        stack.append(i)
    elif len(stack)>1:
        stack.pop()
        x=i-stack[-1]
        if maxlen<x:
            maxlen, count = x, 1
        elif maxlen==x: 
            count+=1
    else:
        stack[0]=i
print(maxlen,count)