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>.
# LUOGU_RID: 126002664
def find_longest_substring(brackets):
    stack = []
    max_length = 0
    count = 0

    for i, bracket in enumerate(brackets):
        if bracket == '(':
            stack.append(i)
        else:
            if stack and brackets[stack[-1]] == '(':
                stack.pop()
                length = i - (stack[-1] if stack else -1)
                if length > max_length:
                    max_length = length
                    count = 1
                elif length == max_length:
                    count += 1
            else:
                stack.append(i)

    if count == 0:
        return "0 1"
    else:
        return f"{max_length} {count}"

# Example usage
brackets = input()
result = find_longest_substring(brackets)
print(result)