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>.
line = input()

res = [0, 1]

left = -2
right = -2
stack = []
for (i, ch) in enumerate(line):
    if ch == '(':
        stack.append(i)
    else:
        if len(stack):
            _left = stack.pop()
            _right = i

            if right+1 == _left:
                right = _right
            elif right+1 < _left or _left < left:
                left, right = _left, _right
            else:
                continue

            length = right-left+1
            if length > res[0]:
                res = [length, 1]
            elif length == res[0]:
                res[1] += 1

print(res[0], res[1])
