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>.
# link: https://codeforces.com/problemset/problem/5/C

sequence = input()
n = len(sequence)
stack = [-1]
max_length = 0
substring_count = 1
for idx in range(n):
    if sequence[idx] == "(":
        stack.append(idx)
    elif len(stack) >= 2:
        stack.pop()
        temp_count = idx - stack[-1]
        if max_length < temp_count:
            max_length = temp_count
            substring_count = 1
        elif max_length == temp_count:
            substring_count += 1 
    else:
        stack[0] = idx
print(max_length, substring_count)                       