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()
stack = []
count = 0
maxc = 0
freq = 0

for b in s:
    if b == ')' and len(stack) != 0:
        stack.pop()
        count += 2
    if b == '(':
        stack.append(b)
        
    if len(stack) == 0:
        if maxc < count:
            maxc = count
            freq = 1
        elif maxc == count:
            freq += 1
        count = 0

if maxc == 0:
    print (0, 1)
else:
    print (maxc, freq)