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>.
bracket_str = input()
stack = [-1]
max_len = 0
max_len_count = 1

for i in range(len(bracket_str)):
    if bracket_str[i] == ')':
        if len(stack) > 1:
            stack.pop()
            cur_len = i - stack[-1]
            if cur_len == max_len:
                max_len_count += 1
            elif cur_len > max_len:
                max_len = cur_len
                max_len_count = 1
        elif len(stack) == 1:
            stack[0] = i
    else:
        stack.append(i)

print(max_len, max_len_count)
