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)
stack = []
d = [-1] * n
c = [-1] * n
longest = 0
subs = 1
for i in range(n):
    if not stack or s[i] == '(':
        stack.append(i)
    else:
        pos = stack[-1]
        if s[pos] == ')':
            if d[pos - 1] != -1:
                d[i] = d[pos - 1]
            else:
                d[i] = pos
            l = i - d[i] + 1
            if l == longest:
                subs += 1
            elif l > longest:
                longest = l
                subs = 1
        stack.pop()
print(longest, end = " ")
print(subs)