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>.
t = input() + ')'
n, m, k, w = 0, 0, 0, 0
for i in t:
    if i == '(':
        n += 1
        w += 1
    else:
        n -= 1
        if n < 0:
            if w > m:
                m = w
                k = 1
            elif w == m:
                k += 1
            w = 0
            n = 0
        else:
            w += 1
if m == 0:
    k = 1
print(m, k)
