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>.
seq = input()

Regular = [0 for _ in range(len(seq))]

stack = []
for index in range(len(seq)):
    if seq[index] == '(':
        stack.append(index)
        continue
    
    if stack == []:
        continue
    left_index = stack[-1]
    stack.pop()
    
    Regular[index] = max(Regular[index], Regular[left_index - 1] + (index - left_index + 1))

max_len = max(Regular)
max_num = Regular.count(max_len)
if max_len == 0:
    print(0, 1)
else:
    print(max_len, max_num)