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().strip()

stack = []
max_len = 0
num_substrings = 0

for i in range(len(s)):
    if s[i] == '(':
        stack.append(i)
    elif len(stack) > 0:
        j = stack.pop()
        if i - j + 1 > max_len:
            max_len = i - j + 1
            num_substrings = 1
        elif i - j + 1 == max_len:
            num_substrings += 1

if max_len == 0:
    print("0 1")
else:
    print(max_len, num_substrings)