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()

m, n = 0, 1
for i in range(len(s) - 1):
    a, c = 0, 0
    for j in range(i, len(s)):
        if s[j] == "(":
            c += 1
        else:
            c -= 1
        if c < 0:
            break
        else:
            a += 1
        if c == 0:
            print(a)
            if a == m:
                n += 1
            elif a > m:
                m = a
                n = 1

print(m, n)