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()

l = -1
n = 1
i = 0

while i < len(s):
    while s[i] == ')':
        i += 1
    o = 0
    c = 0
    while i < len(s):
        if s[i] == '(':
            o += 1
        elif s[i] == ')' and o-c != 0:
            c += 1
        else:
            break
        i += 1
    if l < c:
        l = c
        n = 1
    elif l == c:
        n += 1
print(str(l)+' 'str(n))