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 = len(s)

m = 0
c = 1
l = 0
balanse = 0
for i in range(n):
    if s[i] == "(":
        balanse += 1
    elif s[i] == ")":
        balanse -= 1
    l += 1
    if balanse < 0:
        l = 0
    elif balanse == 0:
        if l > m:
            m = l
            c = 1
        elif l == m:
            c += 1
print(m, c)
