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 = []
i = 0
maxx = 0
d = {}
ans = 0
while i < n:
    if s[i] == ")":
        if stack == []:
            maxx = max(ans, maxx)
            d[maxx] = d.get(maxx, 0)+1
            ans = 0
        else:
            ans = ans+2
            stack.pop()
    else:
        stack.append("(")
    i = i+1
if maxx == 0:
    print(0, 1)
else:
    d[ans] = d.get(ans, 0)+1
    print(maxx, d[maxx])
