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()
res = cnt = 0
stk = [-1]
for i, c in enumerate(s):
    if c == '(':
        stk.append(i)
    else:
        stk.pop()
        if not stk:
            stk.append(i)
        else:
            cur = i-stk[-1]
            if cur>res:
                res = cur
                cnt = 1
            elif cur == res:
                cnt += 1
print(res, cnt)