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 = [-1]
l = 0
rep = 0

for i, c in enumerate(raw_input()):
    if c == '(':
        s.append(i)
    else:
        if len(s) > 1:
            s.pop()
            temp = i - s[-1]
            if temp > l:
                l = temp
                rep = 1
            elif temp == l:
                rep += 1
        else:
            s[0] = i
if l:
    print l, rep
else :
    print 0, 1