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>.
s = input()

n, m = 0, 0

i = 0
while i < len(s):
    if s[i] != '(':
        i += 1
        continue
    a = i
    d = 1
    i += 1
    while d > 0 and i < len(s):
        if s[i] == '(':
            d += 1
        else:
            d -= 1
        i += 1
    if d == 0:
        n += 1
        m = max(m, i - a)

print(m, max(n, 1))
