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>.
x = input()
bal = [0] * len(x)
if x[0] == '(':
    bal[0] = 1
else:
    bal[0] = -1
for i in range(1, len(x)):
    if x[i] == '(':
        bal[i] = bal[i - 1] + 1
    else:
        bal[i] = bal[i - 1] - 1
m_kol = []
for i in range(len(bal)):
    j = i + 1
    kol = 0
    while j < len(bal) and bal[j] >= bal[i]:
        if bal[j] == bal[i]:
            kol = j - i 
        j += 1
    m_kol.append(kol)
ma = max(m_kol)
kol = m_kol.count(ma)
if ma == 0:
    print(0, 1)
else:
    print(ma, kol)