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()
stack = []
ans = 0
c = 0
c1 = 0
for i in range(len(s)):
    if s[i] == "(":
        stack.append(s[i])
        c+=1
    else:
        if len(stack) == 0:
            pass
        else:
            p = stack.pop()
            if len(stack) == 0:
                if ans < (2*c):
                    ans = (2*c)
                    c1 = 1
                elif ans == (2*c):
                    ans = (2*c)
                    c1+=1
                c=0
if ans == 0:
    print(ans,1)
else:
    print(ans,c1)
                    