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>.
a,b,s = 0,1,[-1]
l = enumerate(input())
for i,c in l:
    if (c=='('): s.append(i)
    elif (len(s) > 1):
        s.pop()
        n = i - s[-1]
        if (a < n):
            a = n
            b = 1 
        elif (a == n): b += 1
    else: s[0] = i
print(a,b)